(0) Obligation:
Runtime Complexity TRS:
The TRS R consists of the following rules:
active(U11(tt, V2)) → mark(U12(isNat(V2)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNat(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt, N)) → mark(N)
active(U51(tt, M, N)) → mark(U52(isNat(N), M, N))
active(U52(tt, M, N)) → mark(s(plus(N, M)))
active(U61(tt)) → mark(0)
active(U71(tt, M, N)) → mark(U72(isNat(N), M, N))
active(U72(tt, M, N)) → mark(plus(x(N, M), N))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNat(V1), V2))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNat(x(V1, V2))) → mark(U31(isNat(V1), V2))
active(plus(N, 0)) → mark(U41(isNat(N), N))
active(plus(N, s(M))) → mark(U51(isNat(M), M, N))
active(x(N, 0)) → mark(U61(isNat(N)))
active(x(N, s(M))) → mark(U71(isNat(M), M, N))
active(U11(X1, X2)) → U11(active(X1), X2)
active(U12(X)) → U12(active(X))
active(U21(X)) → U21(active(X))
active(U31(X1, X2)) → U31(active(X1), X2)
active(U32(X)) → U32(active(X))
active(U41(X1, X2)) → U41(active(X1), X2)
active(U51(X1, X2, X3)) → U51(active(X1), X2, X3)
active(U52(X1, X2, X3)) → U52(active(X1), X2, X3)
active(s(X)) → s(active(X))
active(plus(X1, X2)) → plus(active(X1), X2)
active(plus(X1, X2)) → plus(X1, active(X2))
active(U61(X)) → U61(active(X))
active(U71(X1, X2, X3)) → U71(active(X1), X2, X3)
active(U72(X1, X2, X3)) → U72(active(X1), X2, X3)
active(x(X1, X2)) → x(active(X1), X2)
active(x(X1, X2)) → x(X1, active(X2))
U11(mark(X1), X2) → mark(U11(X1, X2))
U12(mark(X)) → mark(U12(X))
U21(mark(X)) → mark(U21(X))
U31(mark(X1), X2) → mark(U31(X1, X2))
U32(mark(X)) → mark(U32(X))
U41(mark(X1), X2) → mark(U41(X1, X2))
U51(mark(X1), X2, X3) → mark(U51(X1, X2, X3))
U52(mark(X1), X2, X3) → mark(U52(X1, X2, X3))
s(mark(X)) → mark(s(X))
plus(mark(X1), X2) → mark(plus(X1, X2))
plus(X1, mark(X2)) → mark(plus(X1, X2))
U61(mark(X)) → mark(U61(X))
U71(mark(X1), X2, X3) → mark(U71(X1, X2, X3))
U72(mark(X1), X2, X3) → mark(U72(X1, X2, X3))
x(mark(X1), X2) → mark(x(X1, X2))
x(X1, mark(X2)) → mark(x(X1, X2))
proper(U11(X1, X2)) → U11(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(U12(X)) → U12(proper(X))
proper(isNat(X)) → isNat(proper(X))
proper(U21(X)) → U21(proper(X))
proper(U31(X1, X2)) → U31(proper(X1), proper(X2))
proper(U32(X)) → U32(proper(X))
proper(U41(X1, X2)) → U41(proper(X1), proper(X2))
proper(U51(X1, X2, X3)) → U51(proper(X1), proper(X2), proper(X3))
proper(U52(X1, X2, X3)) → U52(proper(X1), proper(X2), proper(X3))
proper(s(X)) → s(proper(X))
proper(plus(X1, X2)) → plus(proper(X1), proper(X2))
proper(U61(X)) → U61(proper(X))
proper(0) → ok(0)
proper(U71(X1, X2, X3)) → U71(proper(X1), proper(X2), proper(X3))
proper(U72(X1, X2, X3)) → U72(proper(X1), proper(X2), proper(X3))
proper(x(X1, X2)) → x(proper(X1), proper(X2))
U11(ok(X1), ok(X2)) → ok(U11(X1, X2))
U12(ok(X)) → ok(U12(X))
isNat(ok(X)) → ok(isNat(X))
U21(ok(X)) → ok(U21(X))
U31(ok(X1), ok(X2)) → ok(U31(X1, X2))
U32(ok(X)) → ok(U32(X))
U41(ok(X1), ok(X2)) → ok(U41(X1, X2))
U51(ok(X1), ok(X2), ok(X3)) → ok(U51(X1, X2, X3))
U52(ok(X1), ok(X2), ok(X3)) → ok(U52(X1, X2, X3))
s(ok(X)) → ok(s(X))
plus(ok(X1), ok(X2)) → ok(plus(X1, X2))
U61(ok(X)) → ok(U61(X))
U71(ok(X1), ok(X2), ok(X3)) → ok(U71(X1, X2, X3))
U72(ok(X1), ok(X2), ok(X3)) → ok(U72(X1, X2, X3))
x(ok(X1), ok(X2)) → ok(x(X1, X2))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
Rewrite Strategy: INNERMOST
(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)
Converted Cpx (relative) TRS to CDT
(2) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
isNat(ok(z0)) → ok(isNat(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0))
ACTIVE(U12(tt)) → c1
ACTIVE(U21(tt)) → c2
ACTIVE(U31(tt, z0)) → c3(U32'(isNat(z0)), ISNAT(z0))
ACTIVE(U32(tt)) → c4
ACTIVE(U41(tt, z0)) → c5
ACTIVE(U51(tt, z0, z1)) → c6(U52'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c7(S(plus(z1, z0)), PLUS(z1, z0))
ACTIVE(U61(tt)) → c8
ACTIVE(U71(tt, z0, z1)) → c9(U72'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c10(PLUS(x(z1, z0), z1), X(z1, z0))
ACTIVE(isNat(0)) → c11
ACTIVE(isNat(plus(z0, z1))) → c12(U11'(isNat(z0), z1), ISNAT(z0))
ACTIVE(isNat(s(z0))) → c13(U21'(isNat(z0)), ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c14(U31'(isNat(z0), z1), ISNAT(z0))
ACTIVE(plus(z0, 0)) → c15(U41'(isNat(z0), z0), ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(U51'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(x(z0, 0)) → c17(U61'(isNat(z0)), ISNAT(z0))
ACTIVE(x(z0, s(z1))) → c18(U71'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(tt) → c66
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(0) → c78
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
S tuples:
ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0))
ACTIVE(U12(tt)) → c1
ACTIVE(U21(tt)) → c2
ACTIVE(U31(tt, z0)) → c3(U32'(isNat(z0)), ISNAT(z0))
ACTIVE(U32(tt)) → c4
ACTIVE(U41(tt, z0)) → c5
ACTIVE(U51(tt, z0, z1)) → c6(U52'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c7(S(plus(z1, z0)), PLUS(z1, z0))
ACTIVE(U61(tt)) → c8
ACTIVE(U71(tt, z0, z1)) → c9(U72'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c10(PLUS(x(z1, z0), z1), X(z1, z0))
ACTIVE(isNat(0)) → c11
ACTIVE(isNat(plus(z0, z1))) → c12(U11'(isNat(z0), z1), ISNAT(z0))
ACTIVE(isNat(s(z0))) → c13(U21'(isNat(z0)), ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c14(U31'(isNat(z0), z1), ISNAT(z0))
ACTIVE(plus(z0, 0)) → c15(U41'(isNat(z0), z0), ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(U51'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(x(z0, 0)) → c17(U61'(isNat(z0)), ISNAT(z0))
ACTIVE(x(z0, s(z1))) → c18(U71'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(tt) → c66
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(0) → c78
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:
active, U11, U12, U21, U31, U32, U41, U51, U52, s, plus, U61, U71, U72, x, proper, isNat, top
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84
(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 8 trailing nodes:
ACTIVE(isNat(0)) → c11
ACTIVE(U12(tt)) → c1
ACTIVE(U41(tt, z0)) → c5
PROPER(tt) → c66
ACTIVE(U21(tt)) → c2
ACTIVE(U32(tt)) → c4
PROPER(0) → c78
ACTIVE(U61(tt)) → c8
(4) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
isNat(ok(z0)) → ok(isNat(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0))
ACTIVE(U31(tt, z0)) → c3(U32'(isNat(z0)), ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c6(U52'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c7(S(plus(z1, z0)), PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c9(U72'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c10(PLUS(x(z1, z0), z1), X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c12(U11'(isNat(z0), z1), ISNAT(z0))
ACTIVE(isNat(s(z0))) → c13(U21'(isNat(z0)), ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c14(U31'(isNat(z0), z1), ISNAT(z0))
ACTIVE(plus(z0, 0)) → c15(U41'(isNat(z0), z0), ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(U51'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(x(z0, 0)) → c17(U61'(isNat(z0)), ISNAT(z0))
ACTIVE(x(z0, s(z1))) → c18(U71'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
S tuples:
ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0))
ACTIVE(U31(tt, z0)) → c3(U32'(isNat(z0)), ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c6(U52'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c7(S(plus(z1, z0)), PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c9(U72'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c10(PLUS(x(z1, z0), z1), X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c12(U11'(isNat(z0), z1), ISNAT(z0))
ACTIVE(isNat(s(z0))) → c13(U21'(isNat(z0)), ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c14(U31'(isNat(z0), z1), ISNAT(z0))
ACTIVE(plus(z0, 0)) → c15(U41'(isNat(z0), z0), ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(U51'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(x(z0, 0)) → c17(U61'(isNat(z0)), ISNAT(z0))
ACTIVE(x(z0, s(z1))) → c18(U71'(isNat(z1), z1, z0), ISNAT(z1))
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:
active, U11, U12, U21, U31, U32, U41, U51, U52, s, plus, U61, U71, U72, x, proper, isNat, top
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c, c3, c6, c7, c9, c10, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84
(5) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(6) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
isNat(ok(z0)) → ok(isNat(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0))
ACTIVE(U31(tt, z0)) → c3(U32'(isNat(z0)), ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c6(U52'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c7(S(plus(z1, z0)), PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c9(U72'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c10(PLUS(x(z1, z0), z1), X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c12(U11'(isNat(z0), z1), ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c14(U31'(isNat(z0), z1), ISNAT(z0))
ACTIVE(plus(z0, 0)) → c15(U41'(isNat(z0), z0), ISNAT(z0))
ACTIVE(x(z0, 0)) → c17(U61'(isNat(z0)), ISNAT(z0))
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
S tuples:
ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0))
ACTIVE(U31(tt, z0)) → c3(U32'(isNat(z0)), ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c6(U52'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c7(S(plus(z1, z0)), PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c9(U72'(isNat(z1), z0, z1), ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c10(PLUS(x(z1, z0), z1), X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c12(U11'(isNat(z0), z1), ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c14(U31'(isNat(z0), z1), ISNAT(z0))
ACTIVE(plus(z0, 0)) → c15(U41'(isNat(z0), z0), ISNAT(z0))
ACTIVE(x(z0, 0)) → c17(U61'(isNat(z0)), ISNAT(z0))
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
K tuples:none
Defined Rule Symbols:
active, U11, U12, U21, U31, U32, U41, U51, U52, s, plus, U61, U71, U72, x, proper, isNat, top
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c, c3, c6, c7, c9, c10, c12, c14, c15, c17, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18
(7) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(8) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
isNat(ok(z0)) → ok(isNat(z0))
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
Tuples:
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
S tuples:
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
K tuples:none
Defined Rule Symbols:
active, U11, U12, U21, U31, U32, U41, U51, U52, s, plus, U61, U71, U72, x, proper, isNat, top
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1
(9) CdtUsableRulesProof (EQUIVALENT transformation)
The following rules are not usable and were removed:
top(mark(z0)) → top(proper(z0))
top(ok(z0)) → top(active(z0))
(10) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
S tuples:
ACTIVE(U11(z0, z1)) → c19(U11'(active(z0), z1), ACTIVE(z0))
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1
(11) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U11(
z0,
z1)) →
c19(
U11'(
active(
z0),
z1),
ACTIVE(
z0)) by
ACTIVE(U11(U11(tt, z0), x1)) → c19(U11'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c19(U11'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c19(U11'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c19(U11'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
(12) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U11(tt, z0), x1)) → c19(U11'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c19(U11'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c19(U11'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c19(U11'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U11(tt, z0), x1)) → c19(U11'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c19(U11'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c19(U11'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c19(U11'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19
(13) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 1 trailing tuple parts
(14) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U11(tt, z0), x1)) → c19(U11'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c19(U11'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c19(U11'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c19(U11'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
S tuples:
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U11(tt, z0), x1)) → c19(U11'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c19(U11'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c19(U11'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c19(U11'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19
(15) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(16) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(U12(z0)) → c20(U12'(active(z0)), ACTIVE(z0))
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c
(17) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U12(
z0)) →
c20(
U12'(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(U12(U11(tt, z0))) → c20(U12'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c20(U12'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c20(U12'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c20(U12'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
(18) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U11(tt, z0))) → c20(U12'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c20(U12'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c20(U12'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c20(U12'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U11(tt, z0))) → c20(U12'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c20(U12'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c20(U12'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c20(U12'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20
(19) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(20) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U11(tt, z0))) → c20(U12'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c20(U12'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c20(U12'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c20(U12'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
S tuples:
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U11(tt, z0))) → c20(U12'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c20(U12'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c20(U12'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c20(U12'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20
(21) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(22) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(U21(z0)) → c21(U21'(active(z0)), ACTIVE(z0))
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2
(23) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U21(
z0)) →
c21(
U21'(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(U21(U11(tt, z0))) → c21(U21'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c21(U21'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c21(U21'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c21(U21'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
(24) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U11(tt, z0))) → c21(U21'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c21(U21'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c21(U21'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c21(U21'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U11(tt, z0))) → c21(U21'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c21(U21'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c21(U21'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c21(U21'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21
(25) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 5 trailing tuple parts
(26) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U11(tt, z0))) → c21(U21'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c21(U21'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c21(U21'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c21(U21'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
S tuples:
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U11(tt, z0))) → c21(U21'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c21(U21'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c21(U21'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c21(U21'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21
(27) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(28) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(U31(z0, z1)) → c22(U31'(active(z0), z1), ACTIVE(z0))
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3
(29) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U31(
z0,
z1)) →
c22(
U31'(
active(
z0),
z1),
ACTIVE(
z0)) by
ACTIVE(U31(U11(tt, z0), x1)) → c22(U31'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U31(U31(tt, z0), x1)) → c22(U31'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c22(U31'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c22(U31'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c22(U31'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
(30) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U11(tt, z0), x1)) → c22(U31'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U31(U31(tt, z0), x1)) → c22(U31'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c22(U31'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c22(U31'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c22(U31'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U11(tt, z0), x1)) → c22(U31'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U31(U31(tt, z0), x1)) → c22(U31'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c22(U31'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c22(U31'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c22(U31'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22
(31) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 3 trailing tuple parts
(32) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U11(tt, z0), x1)) → c22(U31'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c22(U31'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c22(U31'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c22(U31'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c22(U31'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
S tuples:
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U31(tt, z0), x1)) → c19(U11'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U31(tt, z0))) → c20(U12'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U31(tt, z0))) → c21(U21'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U11(tt, z0), x1)) → c22(U31'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c22(U31'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c22(U31'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c22(U31'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c22(U31'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22
(33) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(34) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(U32(z0)) → c23(U32'(active(z0)), ACTIVE(z0))
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4
(35) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U32(
z0)) →
c23(
U32'(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(U32(U11(tt, z0))) → c23(U32'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U32(U31(tt, z0))) → c23(U32'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c23(U32'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c23(U32'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c23(U32'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
(36) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U11(tt, z0))) → c23(U32'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U32(U31(tt, z0))) → c23(U32'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c23(U32'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c23(U32'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c23(U32'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U11(tt, z0))) → c23(U32'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U32(U31(tt, z0))) → c23(U32'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c23(U32'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c23(U32'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c23(U32'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23
(37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 8 trailing tuple parts
(38) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U11(tt, z0))) → c23(U32'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c23(U32'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c23(U32'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c23(U32'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c23(U32'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
S tuples:
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U11(tt, z0))) → c23(U32'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c23(U32'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c23(U32'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c23(U32'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c23(U32'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23
(39) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(40) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(U41(z0, z1)) → c24(U41'(active(z0), z1), ACTIVE(z0))
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5
(41) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U41(
z0,
z1)) →
c24(
U41'(
active(
z0),
z1),
ACTIVE(
z0)) by
ACTIVE(U41(U11(tt, z0), x1)) → c24(U41'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U41(U31(tt, z0), x1)) → c24(U41'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c24(U41'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c24(U41'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c24(U41'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
(42) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U11(tt, z0), x1)) → c24(U41'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U41(U31(tt, z0), x1)) → c24(U41'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c24(U41'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c24(U41'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c24(U41'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U11(tt, z0), x1)) → c24(U41'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U12(tt)))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U21(tt)))
ACTIVE(U41(U31(tt, z0), x1)) → c24(U41'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1), ACTIVE(U32(tt)))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1), ACTIVE(U41(tt, z0)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1), ACTIVE(isNat(0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c24(U41'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c24(U41'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c24(U41'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24
(43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 10 trailing tuple parts
(44) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U11(tt, z0), x1)) → c24(U41'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c24(U41'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c24(U41'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c24(U41'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c24(U41'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
S tuples:
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U11(tt, z0), x1)) → c24(U41'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c24(U41'(mark(U32(isNat(z0))), x1), ACTIVE(U31(tt, z0)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c24(U41'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c24(U41'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c24(U41'(mark(U31(isNat(z0), z1)), x1), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24
(45) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(46) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(U51(z0, z1, z2)) → c25(U51'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6
(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U51(
z0,
z1,
z2)) →
c25(
U51'(
active(
z0),
z1,
z2),
ACTIVE(
z0)) by
ACTIVE(U51(U11(tt, z0), x1, x2)) → c25(U51'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U12(tt)))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U21(tt)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c25(U51'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U32(tt)))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2), ACTIVE(U41(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c25(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c25(U51'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(isNat(0)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c25(U51'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c25(U51'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c25(U51'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
(48) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c25(U51'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U12(tt)))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U21(tt)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c25(U51'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U32(tt)))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2), ACTIVE(U41(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c25(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c25(U51'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(isNat(0)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c25(U51'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c25(U51'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c25(U51'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c25(U51'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U12(tt)))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U21(tt)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c25(U51'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(U32(tt)))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2), ACTIVE(U41(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c25(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c25(U51'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2), ACTIVE(isNat(0)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c25(U51'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c25(U51'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c25(U51'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25
(49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 5 trailing tuple parts
(50) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c25(U51'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c25(U51'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c25(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c25(U51'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c25(U51'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c25(U51'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c25(U51'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
S tuples:
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c19(U11'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c20(U12'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c21(U21'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c22(U31'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c23(U32'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c24(U41'(mark(U52(isNat(z1), z0, z1)), x1), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c25(U51'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c25(U51'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c25(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c25(U51'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c25(U51'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c25(U51'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c25(U51'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25
(51) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(52) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c25(U51'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(U52(z0, z1, z2)) → c26(U52'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c25(U51'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7
(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U52(
z0,
z1,
z2)) →
c26(
U52'(
active(
z0),
z1,
z2),
ACTIVE(
z0)) by
ACTIVE(U52(U11(tt, z0), x1, x2)) → c26(U52'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2), ACTIVE(U12(tt)))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2), ACTIVE(U21(tt)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c26(U52'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2), ACTIVE(U32(tt)))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2), ACTIVE(U41(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c26(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c26(U52'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2), ACTIVE(isNat(0)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c26(U52'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c26(U52'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c26(U52'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
(54) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c25(U51'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c26(U52'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2), ACTIVE(U12(tt)))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2), ACTIVE(U21(tt)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c26(U52'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2), ACTIVE(U32(tt)))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2), ACTIVE(U41(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c26(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c26(U52'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2), ACTIVE(isNat(0)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c26(U52'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c26(U52'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c26(U52'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c25(U51'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c26(U52'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2), ACTIVE(U12(tt)))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2), ACTIVE(U21(tt)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c26(U52'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2), ACTIVE(U32(tt)))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2), ACTIVE(U41(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c26(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c26(U52'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2), ACTIVE(isNat(0)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c26(U52'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c26(U52'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c26(U52'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26
(55) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 5 trailing tuple parts
(56) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c25(U51'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c26(U52'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c26(U52'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c26(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c26(U52'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c26(U52'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c26(U52'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c26(U52'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
S tuples:
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c19(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U52(tt, z0, z1))) → c20(U12'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U52(tt, z0, z1))) → c21(U21'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c22(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U52(tt, z0, z1))) → c23(U32'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c24(U41'(mark(s(plus(z1, z0))), x1), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c25(U51'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c26(U52'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c26(U52'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c26(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c26(U52'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c26(U52'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c26(U52'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c26(U52'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26
(57) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(58) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(s(z0)) → c27(S(active(z0)), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8
(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
s(
z0)) →
c27(
S(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(s(U11(tt, z0))) → c27(S(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(s(U31(tt, z0))) → c27(S(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c27(S(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c27(S(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(U61(tt))) → c27(S(mark(0)), ACTIVE(U61(tt)))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(s(isNat(plus(z0, z1)))) → c27(S(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c27(S(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c27(S(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
(60) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U11(tt, z0))) → c27(S(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(s(U31(tt, z0))) → c27(S(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c27(S(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c27(S(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(U61(tt))) → c27(S(mark(0)), ACTIVE(U61(tt)))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(s(isNat(plus(z0, z1)))) → c27(S(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c27(S(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c27(S(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U11(tt, z0))) → c27(S(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(s(U31(tt, z0))) → c27(S(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c27(S(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c27(S(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(U61(tt))) → c27(S(mark(0)), ACTIVE(U61(tt)))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(s(isNat(plus(z0, z1)))) → c27(S(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c27(S(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c27(S(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27
(61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 5 trailing tuple parts
(62) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U11(tt, z0))) → c27(S(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c27(S(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c27(S(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c27(S(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(U61(tt))) → c27(S(mark(0)), ACTIVE(U61(tt)))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c27(S(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c27(S(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c27(S(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U11(tt, z0))) → c27(S(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c27(S(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c27(S(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c27(S(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(U61(tt))) → c27(S(mark(0)), ACTIVE(U61(tt)))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c27(S(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c27(S(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c27(S(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27
(63) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(64) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U61(tt))) → c27(S(mark(0)), ACTIVE(U61(tt)))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U61(z0)) → c30(U61'(active(z0)), ACTIVE(z0))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U61(tt))) → c27(S(mark(0)), ACTIVE(U61(tt)))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9
(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U61(
z0)) →
c30(
U61'(
active(
z0)),
ACTIVE(
z0)) by
ACTIVE(U61(U11(tt, z0))) → c30(U61'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U61(U31(tt, z0))) → c30(U61'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c30(U61'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c30(U61'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U61(U71(tt, z0, z1))) → c30(U61'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c30(U61'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c30(U61'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c30(U61'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
(66) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U61(tt))) → c27(S(mark(0)), ACTIVE(U61(tt)))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U11(tt, z0))) → c30(U61'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U61(U31(tt, z0))) → c30(U61'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c30(U61'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c30(U61'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U61(U71(tt, z0, z1))) → c30(U61'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c30(U61'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c30(U61'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c30(U61'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1), ACTIVE(U61(tt)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U61(tt))) → c27(S(mark(0)), ACTIVE(U61(tt)))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U11(tt, z0))) → c30(U61'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)), ACTIVE(U12(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)), ACTIVE(U21(tt)))
ACTIVE(U61(U31(tt, z0))) → c30(U61'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)), ACTIVE(U32(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)), ACTIVE(U41(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c30(U61'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c30(U61'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)), ACTIVE(U61(tt)))
ACTIVE(U61(U71(tt, z0, z1))) → c30(U61'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)), ACTIVE(isNat(0)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c30(U61'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c30(U61'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c30(U61'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30
(67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 15 trailing tuple parts
(68) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U11(tt, z0))) → c30(U61'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c30(U61'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c30(U61'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c30(U61'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c30(U61'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c30(U61'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c30(U61'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c30(U61'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U11(tt, z0))) → c30(U61'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c30(U61'(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c30(U61'(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c30(U61'(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c30(U61'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c30(U61'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c30(U61'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c30(U61'(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30
(69) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(70) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c30(U61'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U71(z0, z1, z2)) → c31(U71'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c30(U61'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10
(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U71(
z0,
z1,
z2)) →
c31(
U71'(
active(
z0),
z1,
z2),
ACTIVE(
z0)) by
ACTIVE(U71(U11(tt, z0), x1, x2)) → c31(U71'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2), ACTIVE(U12(tt)))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2), ACTIVE(U21(tt)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c31(U71'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2), ACTIVE(U32(tt)))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2), ACTIVE(U41(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c31(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c31(U71'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c31(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c31(U71'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2), ACTIVE(isNat(0)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c31(U71'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c31(U71'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c31(U71'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
(72) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c30(U61'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c31(U71'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2), ACTIVE(U12(tt)))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2), ACTIVE(U21(tt)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c31(U71'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2), ACTIVE(U32(tt)))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2), ACTIVE(U41(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c31(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c31(U71'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c31(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c31(U71'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2), ACTIVE(isNat(0)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c31(U71'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c31(U71'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c31(U71'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c30(U61'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c31(U71'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2), ACTIVE(U12(tt)))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2), ACTIVE(U21(tt)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c31(U71'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2), ACTIVE(U32(tt)))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2), ACTIVE(U41(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c31(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c31(U71'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c31(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c31(U71'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2), ACTIVE(isNat(0)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c31(U71'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c31(U71'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c31(U71'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31
(73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(74) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c30(U61'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c31(U71'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c31(U71'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c31(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c31(U71'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c31(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c31(U71'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c31(U71'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c31(U71'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c31(U71'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c19(U11'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c20(U12'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c21(U21'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c22(U31'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c23(U32'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c24(U41'(mark(U72(isNat(z1), z0, z1)), x1), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c25(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c26(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c27(S(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c30(U61'(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c31(U71'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c31(U71'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c31(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c31(U71'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c31(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c31(U71'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c31(U71'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c31(U71'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c31(U71'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31
(75) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(76) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c31(U71'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(U72(z0, z1, z2)) → c32(U72'(active(z0), z1, z2), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c31(U71'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11
(77) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
ACTIVE(
U72(
z0,
z1,
z2)) →
c32(
U72'(
active(
z0),
z1,
z2),
ACTIVE(
z0)) by
ACTIVE(U72(U11(tt, z0), x1, x2)) → c32(U72'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2), ACTIVE(U12(tt)))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2), ACTIVE(U21(tt)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c32(U72'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2), ACTIVE(U32(tt)))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2), ACTIVE(U41(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c32(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c32(U72'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c32(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c32(U72'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2), ACTIVE(isNat(0)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c32(U72'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c32(U72'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c32(U72'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
(78) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c31(U71'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c32(U72'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2), ACTIVE(U12(tt)))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2), ACTIVE(U21(tt)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c32(U72'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2), ACTIVE(U32(tt)))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2), ACTIVE(U41(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c32(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c32(U72'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c32(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c32(U72'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2), ACTIVE(isNat(0)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c32(U72'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c32(U72'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c32(U72'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c31(U71'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c32(U72'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2), ACTIVE(U12(tt)))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2), ACTIVE(U21(tt)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c32(U72'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2), ACTIVE(U32(tt)))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2), ACTIVE(U41(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c32(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c32(U72'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2), ACTIVE(U61(tt)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c32(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c32(U72'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2), ACTIVE(isNat(0)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c32(U72'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c32(U72'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c32(U72'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32
(79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(80) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c31(U71'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c32(U72'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c32(U72'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c32(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c32(U72'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c32(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c32(U72'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c32(U72'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c32(U72'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c32(U72'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c19(U11'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c20(U12'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c21(U21'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c22(U31'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c23(U32'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c24(U41'(mark(plus(x(z1, z0), z1)), x1), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c25(U51'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c26(U52'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(U72(tt, z0, z1))) → c27(S(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c30(U61'(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c31(U71'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c32(U72'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c32(U72'(mark(U32(isNat(z0))), x1, x2), ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c32(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2), ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c32(U72'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c32(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2), ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c32(U72'(mark(plus(x(z1, z0), z1)), x1, x2), ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c32(U72'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c32(U72'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c32(U72'(mark(U31(isNat(z0), z1)), x1, x2), ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32
(81) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)
Split RHS of tuples not part of any SCC
(82) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U11(z0, z1)) → c65(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12
(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
U11(
z0,
z1)) →
c65(
U11'(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
(84) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65
(85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
(86) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U12(z0)) → c67(U12'(proper(z0)), PROPER(z0))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65
(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
U12(
z0)) →
c67(
U12'(
proper(
z0)),
PROPER(
z0)) by
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)), PROPER(tt))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(0)) → c67(U12'(ok(0)), PROPER(0))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
(88) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)), PROPER(tt))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(0)) → c67(U12'(ok(0)), PROPER(0))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)), PROPER(tt))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(0)) → c67(U12'(ok(0)), PROPER(0))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67
(89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
(90) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(isNat(z0)) → c68(ISNAT(proper(z0)), PROPER(z0))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67
(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
isNat(
z0)) →
c68(
ISNAT(
proper(
z0)),
PROPER(
z0)) by
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)), PROPER(tt))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)), PROPER(0))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
(92) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)), PROPER(tt))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)), PROPER(0))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)), PROPER(tt))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)), PROPER(0))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68
(93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
(94) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U21(z0)) → c69(U21'(proper(z0)), PROPER(z0))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c69, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68
(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
U21(
z0)) →
c69(
U21'(
proper(
z0)),
PROPER(
z0)) by
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)), PROPER(tt))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(0)) → c69(U21'(ok(0)), PROPER(0))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
(96) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)), PROPER(tt))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(0)) → c69(U21'(ok(0)), PROPER(0))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)), PROPER(tt))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(0)) → c69(U21'(ok(0)), PROPER(0))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69
(97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
(98) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U31(z0, z1)) → c70(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c70, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69
(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
U31(
z0,
z1)) →
c70(
U31'(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
(100) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70
(101) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
(102) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U32(z0)) → c71(U32'(proper(z0)), PROPER(z0))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c71, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70
(103) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
U32(
z0)) →
c71(
U32'(
proper(
z0)),
PROPER(
z0)) by
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)), PROPER(tt))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(0)) → c71(U32'(ok(0)), PROPER(0))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
(104) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)), PROPER(tt))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(0)) → c71(U32'(ok(0)), PROPER(0))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)), PROPER(tt))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(0)) → c71(U32'(ok(0)), PROPER(0))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71
(105) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
(106) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U41(z0, z1)) → c72(U41'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c72, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71
(107) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
U41(
z0,
z1)) →
c72(
U41'(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
(108) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72
(109) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
(110) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U51(z0, z1, z2)) → c73(U51'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c73, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72
(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
U51(
z0,
z1,
z2)) →
c73(
U51'(
proper(
z0),
proper(
z1),
proper(
z2)),
PROPER(
z0),
PROPER(
z1),
PROPER(
z2)) by
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
(112) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73
(113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(114) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U52(z0, z1, z2)) → c74(U52'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c74, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73
(115) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
U52(
z0,
z1,
z2)) →
c74(
U52'(
proper(
z0),
proper(
z1),
proper(
z2)),
PROPER(
z0),
PROPER(
z1),
PROPER(
z2)) by
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
(116) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74
(117) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(118) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(s(z0)) → c75(S(proper(z0)), PROPER(z0))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c75, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74
(119) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
s(
z0)) →
c75(
S(
proper(
z0)),
PROPER(
z0)) by
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)), PROPER(tt))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(0)) → c75(S(ok(0)), PROPER(0))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
(120) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)), PROPER(tt))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(0)) → c75(S(ok(0)), PROPER(0))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)), PROPER(tt))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(0)) → c75(S(ok(0)), PROPER(0))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75
(121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
(122) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(plus(z0, z1)) → c76(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c76, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75
(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
plus(
z0,
z1)) →
c76(
PLUS(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
(124) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76
(125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
(126) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U61(z0)) → c77(U61'(proper(z0)), PROPER(z0))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c77, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76
(127) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
U61(
z0)) →
c77(
U61'(
proper(
z0)),
PROPER(
z0)) by
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)), PROPER(tt))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(0)) → c77(U61'(ok(0)), PROPER(0))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
(128) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)), PROPER(tt))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(0)) → c77(U61'(ok(0)), PROPER(0))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)), PROPER(tt))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(0)) → c77(U61'(ok(0)), PROPER(0))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77
(129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
(130) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U71(z0, z1, z2)) → c79(U71'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c79, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77
(131) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
U71(
z0,
z1,
z2)) →
c79(
U71'(
proper(
z0),
proper(
z1),
proper(
z2)),
PROPER(
z0),
PROPER(
z1),
PROPER(
z2)) by
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
(132) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77, c79
(133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(134) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(U72(z0, z1, z2)) → c80(U72'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c80, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77, c79, c79
(135) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
U72(
z0,
z1,
z2)) →
c80(
U72'(
proper(
z0),
proper(
z1),
proper(
z2)),
PROPER(
z0),
PROPER(
z1),
PROPER(
z2)) by
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
(136) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77, c79, c79, c80
(137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 6 trailing tuple parts
(138) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
PROPER(x(z0, z1)) → c81(X(proper(z0), proper(z1)), PROPER(z0), PROPER(z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, PROPER, ISNAT, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c81, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77, c79, c79, c80, c80
(139) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
PROPER(
x(
z0,
z1)) →
c81(
X(
proper(
z0),
proper(
z1)),
PROPER(
z0),
PROPER(
z1)) by
PROPER(x(x0, U11(z0, z1))) → c81(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(x(x0, tt)) → c81(X(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(x(x0, U12(z0))) → c81(X(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(x(x0, isNat(z0))) → c81(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(x(x0, U21(z0))) → c81(X(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(x(x0, U31(z0, z1))) → c81(X(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(x(x0, U32(z0))) → c81(X(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(x(x0, U41(z0, z1))) → c81(X(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(x(x0, U51(z0, z1, z2))) → c81(X(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(x(x0, U52(z0, z1, z2))) → c81(X(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(x(x0, s(z0))) → c81(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(x(x0, plus(z0, z1))) → c81(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(x(x0, U61(z0))) → c81(X(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(x(x0, 0)) → c81(X(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(x(x0, U71(z0, z1, z2))) → c81(X(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(x(x0, U72(z0, z1, z2))) → c81(X(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(x(x0, x(z0, z1))) → c81(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(x(U11(z0, z1), x1)) → c81(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(x(tt, x1)) → c81(X(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(x(U12(z0), x1)) → c81(X(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(x(isNat(z0), x1)) → c81(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(x(U21(z0), x1)) → c81(X(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(x(U31(z0, z1), x1)) → c81(X(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(x(U32(z0), x1)) → c81(X(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(x(U41(z0, z1), x1)) → c81(X(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(x(U51(z0, z1, z2), x1)) → c81(X(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(x(U52(z0, z1, z2), x1)) → c81(X(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(x(s(z0), x1)) → c81(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(x(plus(z0, z1), x1)) → c81(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(x(U61(z0), x1)) → c81(X(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(x(0, x1)) → c81(X(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(x(U71(z0, z1, z2), x1)) → c81(X(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(x(U72(z0, z1, z2), x1)) → c81(X(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(x(x(z0, z1), x1)) → c81(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
(140) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(x(x0, U11(z0, z1))) → c81(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(x(x0, tt)) → c81(X(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(x(x0, U12(z0))) → c81(X(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(x(x0, isNat(z0))) → c81(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(x(x0, U21(z0))) → c81(X(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(x(x0, U31(z0, z1))) → c81(X(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(x(x0, U32(z0))) → c81(X(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(x(x0, U41(z0, z1))) → c81(X(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(x(x0, U51(z0, z1, z2))) → c81(X(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(x(x0, U52(z0, z1, z2))) → c81(X(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(x(x0, s(z0))) → c81(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(x(x0, plus(z0, z1))) → c81(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(x(x0, U61(z0))) → c81(X(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(x(x0, 0)) → c81(X(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(x(x0, U71(z0, z1, z2))) → c81(X(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(x(x0, U72(z0, z1, z2))) → c81(X(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(x(x0, x(z0, z1))) → c81(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(x(U11(z0, z1), x1)) → c81(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(x(tt, x1)) → c81(X(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(x(U12(z0), x1)) → c81(X(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(x(isNat(z0), x1)) → c81(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(x(U21(z0), x1)) → c81(X(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(x(U31(z0, z1), x1)) → c81(X(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(x(U32(z0), x1)) → c81(X(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(x(U41(z0, z1), x1)) → c81(X(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(x(U51(z0, z1, z2), x1)) → c81(X(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(x(U52(z0, z1, z2), x1)) → c81(X(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(x(s(z0), x1)) → c81(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(x(plus(z0, z1), x1)) → c81(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(x(U61(z0), x1)) → c81(X(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(x(0, x1)) → c81(X(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(x(U71(z0, z1, z2), x1)) → c81(X(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(x(U72(z0, z1, z2), x1)) → c81(X(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(x(x(z0, z1), x1)) → c81(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(x(x0, U11(z0, z1))) → c81(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(x(x0, tt)) → c81(X(proper(x0), ok(tt)), PROPER(x0), PROPER(tt))
PROPER(x(x0, U12(z0))) → c81(X(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(x(x0, isNat(z0))) → c81(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(x(x0, U21(z0))) → c81(X(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(x(x0, U31(z0, z1))) → c81(X(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(x(x0, U32(z0))) → c81(X(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(x(x0, U41(z0, z1))) → c81(X(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(x(x0, U51(z0, z1, z2))) → c81(X(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(x(x0, U52(z0, z1, z2))) → c81(X(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(x(x0, s(z0))) → c81(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(x(x0, plus(z0, z1))) → c81(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(x(x0, U61(z0))) → c81(X(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(x(x0, 0)) → c81(X(proper(x0), ok(0)), PROPER(x0), PROPER(0))
PROPER(x(x0, U71(z0, z1, z2))) → c81(X(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(x(x0, U72(z0, z1, z2))) → c81(X(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(x(x0, x(z0, z1))) → c81(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(x(U11(z0, z1), x1)) → c81(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(x(tt, x1)) → c81(X(ok(tt), proper(x1)), PROPER(tt), PROPER(x1))
PROPER(x(U12(z0), x1)) → c81(X(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(x(isNat(z0), x1)) → c81(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(x(U21(z0), x1)) → c81(X(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(x(U31(z0, z1), x1)) → c81(X(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(x(U32(z0), x1)) → c81(X(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(x(U41(z0, z1), x1)) → c81(X(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(x(U51(z0, z1, z2), x1)) → c81(X(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(x(U52(z0, z1, z2), x1)) → c81(X(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(x(s(z0), x1)) → c81(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(x(plus(z0, z1), x1)) → c81(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(x(U61(z0), x1)) → c81(X(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(x(0, x1)) → c81(X(ok(0), proper(x1)), PROPER(0), PROPER(x1))
PROPER(x(U71(z0, z1, z2), x1)) → c81(X(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(x(U72(z0, z1, z2), x1)) → c81(X(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(x(x(z0, z1), x1)) → c81(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT, TOP, PROPER
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77, c79, c79, c80, c80, c81
(141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 4 trailing tuple parts
(142) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(x(x0, U11(z0, z1))) → c81(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(x(x0, U12(z0))) → c81(X(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(x(x0, isNat(z0))) → c81(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(x(x0, U21(z0))) → c81(X(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(x(x0, U31(z0, z1))) → c81(X(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(x(x0, U32(z0))) → c81(X(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(x(x0, U41(z0, z1))) → c81(X(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(x(x0, U51(z0, z1, z2))) → c81(X(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(x(x0, U52(z0, z1, z2))) → c81(X(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(x(x0, s(z0))) → c81(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(x(x0, plus(z0, z1))) → c81(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(x(x0, U61(z0))) → c81(X(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(x(x0, U71(z0, z1, z2))) → c81(X(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(x(x0, U72(z0, z1, z2))) → c81(X(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(x(x0, x(z0, z1))) → c81(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(x(U11(z0, z1), x1)) → c81(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(x(U12(z0), x1)) → c81(X(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(x(isNat(z0), x1)) → c81(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(x(U21(z0), x1)) → c81(X(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(x(U31(z0, z1), x1)) → c81(X(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(x(U32(z0), x1)) → c81(X(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(x(U41(z0, z1), x1)) → c81(X(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(x(U51(z0, z1, z2), x1)) → c81(X(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(x(U52(z0, z1, z2), x1)) → c81(X(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(x(s(z0), x1)) → c81(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(x(plus(z0, z1), x1)) → c81(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(x(U61(z0), x1)) → c81(X(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(x(U71(z0, z1, z2), x1)) → c81(X(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(x(U72(z0, z1, z2), x1)) → c81(X(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(x(x(z0, z1), x1)) → c81(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(x(x0, tt)) → c81(X(proper(x0), ok(tt)), PROPER(x0))
PROPER(x(x0, 0)) → c81(X(proper(x0), ok(0)), PROPER(x0))
PROPER(x(tt, x1)) → c81(X(ok(tt), proper(x1)), PROPER(x1))
PROPER(x(0, x1)) → c81(X(ok(0), proper(x1)), PROPER(x1))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(mark(z0)) → c83(TOP(proper(z0)), PROPER(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(x(x0, U11(z0, z1))) → c81(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(x(x0, U12(z0))) → c81(X(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(x(x0, isNat(z0))) → c81(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(x(x0, U21(z0))) → c81(X(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(x(x0, U31(z0, z1))) → c81(X(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(x(x0, U32(z0))) → c81(X(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(x(x0, U41(z0, z1))) → c81(X(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(x(x0, U51(z0, z1, z2))) → c81(X(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(x(x0, U52(z0, z1, z2))) → c81(X(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(x(x0, s(z0))) → c81(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(x(x0, plus(z0, z1))) → c81(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(x(x0, U61(z0))) → c81(X(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(x(x0, U71(z0, z1, z2))) → c81(X(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(x(x0, U72(z0, z1, z2))) → c81(X(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(x(x0, x(z0, z1))) → c81(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(x(U11(z0, z1), x1)) → c81(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(x(U12(z0), x1)) → c81(X(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(x(isNat(z0), x1)) → c81(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(x(U21(z0), x1)) → c81(X(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(x(U31(z0, z1), x1)) → c81(X(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(x(U32(z0), x1)) → c81(X(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(x(U41(z0, z1), x1)) → c81(X(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(x(U51(z0, z1, z2), x1)) → c81(X(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(x(U52(z0, z1, z2), x1)) → c81(X(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(x(s(z0), x1)) → c81(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(x(plus(z0, z1), x1)) → c81(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(x(U61(z0), x1)) → c81(X(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(x(U71(z0, z1, z2), x1)) → c81(X(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(x(U72(z0, z1, z2), x1)) → c81(X(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(x(x(z0, z1), x1)) → c81(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(x(x0, tt)) → c81(X(proper(x0), ok(tt)), PROPER(x0))
PROPER(x(x0, 0)) → c81(X(proper(x0), ok(0)), PROPER(x0))
PROPER(x(tt, x1)) → c81(X(ok(tt), proper(x1)), PROPER(x1))
PROPER(x(0, x1)) → c81(X(ok(0), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT, TOP, PROPER
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82, c83, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77, c79, c79, c80, c80, c81, c81
(143) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
TOP(
mark(
z0)) →
c83(
TOP(
proper(
z0)),
PROPER(
z0)) by
TOP(mark(U11(z0, z1))) → c83(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
TOP(mark(tt)) → c83(TOP(ok(tt)), PROPER(tt))
TOP(mark(U12(z0))) → c83(TOP(U12(proper(z0))), PROPER(U12(z0)))
TOP(mark(isNat(z0))) → c83(TOP(isNat(proper(z0))), PROPER(isNat(z0)))
TOP(mark(U21(z0))) → c83(TOP(U21(proper(z0))), PROPER(U21(z0)))
TOP(mark(U31(z0, z1))) → c83(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
TOP(mark(U32(z0))) → c83(TOP(U32(proper(z0))), PROPER(U32(z0)))
TOP(mark(U41(z0, z1))) → c83(TOP(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
TOP(mark(U51(z0, z1, z2))) → c83(TOP(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
TOP(mark(U52(z0, z1, z2))) → c83(TOP(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
TOP(mark(s(z0))) → c83(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(plus(z0, z1))) → c83(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(U61(z0))) → c83(TOP(U61(proper(z0))), PROPER(U61(z0)))
TOP(mark(0)) → c83(TOP(ok(0)), PROPER(0))
TOP(mark(U71(z0, z1, z2))) → c83(TOP(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
TOP(mark(U72(z0, z1, z2))) → c83(TOP(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
TOP(mark(x(z0, z1))) → c83(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
(144) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(x(x0, U11(z0, z1))) → c81(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(x(x0, U12(z0))) → c81(X(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(x(x0, isNat(z0))) → c81(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(x(x0, U21(z0))) → c81(X(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(x(x0, U31(z0, z1))) → c81(X(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(x(x0, U32(z0))) → c81(X(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(x(x0, U41(z0, z1))) → c81(X(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(x(x0, U51(z0, z1, z2))) → c81(X(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(x(x0, U52(z0, z1, z2))) → c81(X(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(x(x0, s(z0))) → c81(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(x(x0, plus(z0, z1))) → c81(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(x(x0, U61(z0))) → c81(X(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(x(x0, U71(z0, z1, z2))) → c81(X(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(x(x0, U72(z0, z1, z2))) → c81(X(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(x(x0, x(z0, z1))) → c81(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(x(U11(z0, z1), x1)) → c81(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(x(U12(z0), x1)) → c81(X(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(x(isNat(z0), x1)) → c81(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(x(U21(z0), x1)) → c81(X(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(x(U31(z0, z1), x1)) → c81(X(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(x(U32(z0), x1)) → c81(X(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(x(U41(z0, z1), x1)) → c81(X(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(x(U51(z0, z1, z2), x1)) → c81(X(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(x(U52(z0, z1, z2), x1)) → c81(X(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(x(s(z0), x1)) → c81(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(x(plus(z0, z1), x1)) → c81(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(x(U61(z0), x1)) → c81(X(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(x(U71(z0, z1, z2), x1)) → c81(X(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(x(U72(z0, z1, z2), x1)) → c81(X(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(x(x(z0, z1), x1)) → c81(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(x(x0, tt)) → c81(X(proper(x0), ok(tt)), PROPER(x0))
PROPER(x(x0, 0)) → c81(X(proper(x0), ok(0)), PROPER(x0))
PROPER(x(tt, x1)) → c81(X(ok(tt), proper(x1)), PROPER(x1))
PROPER(x(0, x1)) → c81(X(ok(0), proper(x1)), PROPER(x1))
TOP(mark(U11(z0, z1))) → c83(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
TOP(mark(tt)) → c83(TOP(ok(tt)), PROPER(tt))
TOP(mark(U12(z0))) → c83(TOP(U12(proper(z0))), PROPER(U12(z0)))
TOP(mark(isNat(z0))) → c83(TOP(isNat(proper(z0))), PROPER(isNat(z0)))
TOP(mark(U21(z0))) → c83(TOP(U21(proper(z0))), PROPER(U21(z0)))
TOP(mark(U31(z0, z1))) → c83(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
TOP(mark(U32(z0))) → c83(TOP(U32(proper(z0))), PROPER(U32(z0)))
TOP(mark(U41(z0, z1))) → c83(TOP(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
TOP(mark(U51(z0, z1, z2))) → c83(TOP(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
TOP(mark(U52(z0, z1, z2))) → c83(TOP(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
TOP(mark(s(z0))) → c83(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(plus(z0, z1))) → c83(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(U61(z0))) → c83(TOP(U61(proper(z0))), PROPER(U61(z0)))
TOP(mark(0)) → c83(TOP(ok(0)), PROPER(0))
TOP(mark(U71(z0, z1, z2))) → c83(TOP(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
TOP(mark(U72(z0, z1, z2))) → c83(TOP(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
TOP(mark(x(z0, z1))) → c83(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(x(x0, U11(z0, z1))) → c81(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(x(x0, U12(z0))) → c81(X(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(x(x0, isNat(z0))) → c81(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(x(x0, U21(z0))) → c81(X(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(x(x0, U31(z0, z1))) → c81(X(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(x(x0, U32(z0))) → c81(X(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(x(x0, U41(z0, z1))) → c81(X(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(x(x0, U51(z0, z1, z2))) → c81(X(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(x(x0, U52(z0, z1, z2))) → c81(X(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(x(x0, s(z0))) → c81(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(x(x0, plus(z0, z1))) → c81(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(x(x0, U61(z0))) → c81(X(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(x(x0, U71(z0, z1, z2))) → c81(X(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(x(x0, U72(z0, z1, z2))) → c81(X(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(x(x0, x(z0, z1))) → c81(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(x(U11(z0, z1), x1)) → c81(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(x(U12(z0), x1)) → c81(X(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(x(isNat(z0), x1)) → c81(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(x(U21(z0), x1)) → c81(X(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(x(U31(z0, z1), x1)) → c81(X(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(x(U32(z0), x1)) → c81(X(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(x(U41(z0, z1), x1)) → c81(X(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(x(U51(z0, z1, z2), x1)) → c81(X(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(x(U52(z0, z1, z2), x1)) → c81(X(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(x(s(z0), x1)) → c81(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(x(plus(z0, z1), x1)) → c81(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(x(U61(z0), x1)) → c81(X(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(x(U71(z0, z1, z2), x1)) → c81(X(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(x(U72(z0, z1, z2), x1)) → c81(X(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(x(x(z0, z1), x1)) → c81(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(x(x0, tt)) → c81(X(proper(x0), ok(tt)), PROPER(x0))
PROPER(x(x0, 0)) → c81(X(proper(x0), ok(0)), PROPER(x0))
PROPER(x(tt, x1)) → c81(X(ok(tt), proper(x1)), PROPER(x1))
PROPER(x(0, x1)) → c81(X(ok(0), proper(x1)), PROPER(x1))
TOP(mark(U11(z0, z1))) → c83(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
TOP(mark(tt)) → c83(TOP(ok(tt)), PROPER(tt))
TOP(mark(U12(z0))) → c83(TOP(U12(proper(z0))), PROPER(U12(z0)))
TOP(mark(isNat(z0))) → c83(TOP(isNat(proper(z0))), PROPER(isNat(z0)))
TOP(mark(U21(z0))) → c83(TOP(U21(proper(z0))), PROPER(U21(z0)))
TOP(mark(U31(z0, z1))) → c83(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
TOP(mark(U32(z0))) → c83(TOP(U32(proper(z0))), PROPER(U32(z0)))
TOP(mark(U41(z0, z1))) → c83(TOP(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
TOP(mark(U51(z0, z1, z2))) → c83(TOP(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
TOP(mark(U52(z0, z1, z2))) → c83(TOP(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
TOP(mark(s(z0))) → c83(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(plus(z0, z1))) → c83(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(U61(z0))) → c83(TOP(U61(proper(z0))), PROPER(U61(z0)))
TOP(mark(0)) → c83(TOP(ok(0)), PROPER(0))
TOP(mark(U71(z0, z1, z2))) → c83(TOP(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
TOP(mark(U72(z0, z1, z2))) → c83(TOP(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
TOP(mark(x(z0, z1))) → c83(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT, TOP, PROPER
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77, c79, c79, c80, c80, c81, c81, c83
(145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)
Removed 2 trailing tuple parts
(146) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(x(x0, U11(z0, z1))) → c81(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(x(x0, U12(z0))) → c81(X(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(x(x0, isNat(z0))) → c81(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(x(x0, U21(z0))) → c81(X(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(x(x0, U31(z0, z1))) → c81(X(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(x(x0, U32(z0))) → c81(X(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(x(x0, U41(z0, z1))) → c81(X(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(x(x0, U51(z0, z1, z2))) → c81(X(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(x(x0, U52(z0, z1, z2))) → c81(X(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(x(x0, s(z0))) → c81(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(x(x0, plus(z0, z1))) → c81(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(x(x0, U61(z0))) → c81(X(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(x(x0, U71(z0, z1, z2))) → c81(X(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(x(x0, U72(z0, z1, z2))) → c81(X(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(x(x0, x(z0, z1))) → c81(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(x(U11(z0, z1), x1)) → c81(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(x(U12(z0), x1)) → c81(X(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(x(isNat(z0), x1)) → c81(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(x(U21(z0), x1)) → c81(X(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(x(U31(z0, z1), x1)) → c81(X(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(x(U32(z0), x1)) → c81(X(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(x(U41(z0, z1), x1)) → c81(X(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(x(U51(z0, z1, z2), x1)) → c81(X(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(x(U52(z0, z1, z2), x1)) → c81(X(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(x(s(z0), x1)) → c81(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(x(plus(z0, z1), x1)) → c81(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(x(U61(z0), x1)) → c81(X(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(x(U71(z0, z1, z2), x1)) → c81(X(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(x(U72(z0, z1, z2), x1)) → c81(X(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(x(x(z0, z1), x1)) → c81(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(x(x0, tt)) → c81(X(proper(x0), ok(tt)), PROPER(x0))
PROPER(x(x0, 0)) → c81(X(proper(x0), ok(0)), PROPER(x0))
PROPER(x(tt, x1)) → c81(X(ok(tt), proper(x1)), PROPER(x1))
PROPER(x(0, x1)) → c81(X(ok(0), proper(x1)), PROPER(x1))
TOP(mark(U11(z0, z1))) → c83(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
TOP(mark(U12(z0))) → c83(TOP(U12(proper(z0))), PROPER(U12(z0)))
TOP(mark(isNat(z0))) → c83(TOP(isNat(proper(z0))), PROPER(isNat(z0)))
TOP(mark(U21(z0))) → c83(TOP(U21(proper(z0))), PROPER(U21(z0)))
TOP(mark(U31(z0, z1))) → c83(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
TOP(mark(U32(z0))) → c83(TOP(U32(proper(z0))), PROPER(U32(z0)))
TOP(mark(U41(z0, z1))) → c83(TOP(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
TOP(mark(U51(z0, z1, z2))) → c83(TOP(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
TOP(mark(U52(z0, z1, z2))) → c83(TOP(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
TOP(mark(s(z0))) → c83(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(plus(z0, z1))) → c83(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(U61(z0))) → c83(TOP(U61(proper(z0))), PROPER(U61(z0)))
TOP(mark(U71(z0, z1, z2))) → c83(TOP(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
TOP(mark(U72(z0, z1, z2))) → c83(TOP(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
TOP(mark(x(z0, z1))) → c83(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
TOP(mark(tt)) → c83(TOP(ok(tt)))
TOP(mark(0)) → c83(TOP(ok(0)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
TOP(ok(z0)) → c84(TOP(active(z0)), ACTIVE(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(x(x0, U11(z0, z1))) → c81(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(x(x0, U12(z0))) → c81(X(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(x(x0, isNat(z0))) → c81(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(x(x0, U21(z0))) → c81(X(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(x(x0, U31(z0, z1))) → c81(X(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(x(x0, U32(z0))) → c81(X(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(x(x0, U41(z0, z1))) → c81(X(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(x(x0, U51(z0, z1, z2))) → c81(X(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(x(x0, U52(z0, z1, z2))) → c81(X(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(x(x0, s(z0))) → c81(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(x(x0, plus(z0, z1))) → c81(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(x(x0, U61(z0))) → c81(X(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(x(x0, U71(z0, z1, z2))) → c81(X(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(x(x0, U72(z0, z1, z2))) → c81(X(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(x(x0, x(z0, z1))) → c81(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(x(U11(z0, z1), x1)) → c81(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(x(U12(z0), x1)) → c81(X(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(x(isNat(z0), x1)) → c81(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(x(U21(z0), x1)) → c81(X(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(x(U31(z0, z1), x1)) → c81(X(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(x(U32(z0), x1)) → c81(X(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(x(U41(z0, z1), x1)) → c81(X(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(x(U51(z0, z1, z2), x1)) → c81(X(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(x(U52(z0, z1, z2), x1)) → c81(X(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(x(s(z0), x1)) → c81(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(x(plus(z0, z1), x1)) → c81(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(x(U61(z0), x1)) → c81(X(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(x(U71(z0, z1, z2), x1)) → c81(X(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(x(U72(z0, z1, z2), x1)) → c81(X(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(x(x(z0, z1), x1)) → c81(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(x(x0, tt)) → c81(X(proper(x0), ok(tt)), PROPER(x0))
PROPER(x(x0, 0)) → c81(X(proper(x0), ok(0)), PROPER(x0))
PROPER(x(tt, x1)) → c81(X(ok(tt), proper(x1)), PROPER(x1))
PROPER(x(0, x1)) → c81(X(ok(0), proper(x1)), PROPER(x1))
TOP(mark(U11(z0, z1))) → c83(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
TOP(mark(U12(z0))) → c83(TOP(U12(proper(z0))), PROPER(U12(z0)))
TOP(mark(isNat(z0))) → c83(TOP(isNat(proper(z0))), PROPER(isNat(z0)))
TOP(mark(U21(z0))) → c83(TOP(U21(proper(z0))), PROPER(U21(z0)))
TOP(mark(U31(z0, z1))) → c83(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
TOP(mark(U32(z0))) → c83(TOP(U32(proper(z0))), PROPER(U32(z0)))
TOP(mark(U41(z0, z1))) → c83(TOP(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
TOP(mark(U51(z0, z1, z2))) → c83(TOP(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
TOP(mark(U52(z0, z1, z2))) → c83(TOP(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
TOP(mark(s(z0))) → c83(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(plus(z0, z1))) → c83(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(U61(z0))) → c83(TOP(U61(proper(z0))), PROPER(U61(z0)))
TOP(mark(U71(z0, z1, z2))) → c83(TOP(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
TOP(mark(U72(z0, z1, z2))) → c83(TOP(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
TOP(mark(x(z0, z1))) → c83(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
TOP(mark(tt)) → c83(TOP(ok(tt)))
TOP(mark(0)) → c83(TOP(ok(0)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT, TOP, PROPER
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82, c84, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77, c79, c79, c80, c80, c81, c81, c83, c83
(147) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)
Use narrowing to replace
TOP(
ok(
z0)) →
c84(
TOP(
active(
z0)),
ACTIVE(
z0)) by
TOP(ok(U11(tt, z0))) → c84(TOP(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
TOP(ok(U12(tt))) → c84(TOP(mark(tt)), ACTIVE(U12(tt)))
TOP(ok(U21(tt))) → c84(TOP(mark(tt)), ACTIVE(U21(tt)))
TOP(ok(U31(tt, z0))) → c84(TOP(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
TOP(ok(U32(tt))) → c84(TOP(mark(tt)), ACTIVE(U32(tt)))
TOP(ok(U41(tt, z0))) → c84(TOP(mark(z0)), ACTIVE(U41(tt, z0)))
TOP(ok(U51(tt, z0, z1))) → c84(TOP(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
TOP(ok(U52(tt, z0, z1))) → c84(TOP(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
TOP(ok(U61(tt))) → c84(TOP(mark(0)), ACTIVE(U61(tt)))
TOP(ok(U71(tt, z0, z1))) → c84(TOP(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
TOP(ok(U72(tt, z0, z1))) → c84(TOP(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
TOP(ok(isNat(0))) → c84(TOP(mark(tt)), ACTIVE(isNat(0)))
TOP(ok(isNat(plus(z0, z1)))) → c84(TOP(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
TOP(ok(isNat(s(z0)))) → c84(TOP(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
TOP(ok(isNat(x(z0, z1)))) → c84(TOP(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
TOP(ok(plus(z0, 0))) → c84(TOP(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
TOP(ok(plus(z0, s(z1)))) → c84(TOP(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
TOP(ok(x(z0, 0))) → c84(TOP(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
TOP(ok(x(z0, s(z1)))) → c84(TOP(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
TOP(ok(U11(z0, z1))) → c84(TOP(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
TOP(ok(U12(z0))) → c84(TOP(U12(active(z0))), ACTIVE(U12(z0)))
TOP(ok(U21(z0))) → c84(TOP(U21(active(z0))), ACTIVE(U21(z0)))
TOP(ok(U31(z0, z1))) → c84(TOP(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
TOP(ok(U32(z0))) → c84(TOP(U32(active(z0))), ACTIVE(U32(z0)))
TOP(ok(U41(z0, z1))) → c84(TOP(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
TOP(ok(U51(z0, z1, z2))) → c84(TOP(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
TOP(ok(U52(z0, z1, z2))) → c84(TOP(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
TOP(ok(s(z0))) → c84(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(plus(z0, z1))) → c84(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c84(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(U61(z0))) → c84(TOP(U61(active(z0))), ACTIVE(U61(z0)))
TOP(ok(U71(z0, z1, z2))) → c84(TOP(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
TOP(ok(U72(z0, z1, z2))) → c84(TOP(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
TOP(ok(x(z0, z1))) → c84(TOP(x(active(z0), z1)), ACTIVE(x(z0, z1)))
TOP(ok(x(z0, z1))) → c84(TOP(x(z0, active(z1))), ACTIVE(x(z0, z1)))
(148) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(x(x0, U11(z0, z1))) → c81(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(x(x0, U12(z0))) → c81(X(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(x(x0, isNat(z0))) → c81(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(x(x0, U21(z0))) → c81(X(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(x(x0, U31(z0, z1))) → c81(X(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(x(x0, U32(z0))) → c81(X(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(x(x0, U41(z0, z1))) → c81(X(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(x(x0, U51(z0, z1, z2))) → c81(X(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(x(x0, U52(z0, z1, z2))) → c81(X(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(x(x0, s(z0))) → c81(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(x(x0, plus(z0, z1))) → c81(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(x(x0, U61(z0))) → c81(X(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(x(x0, U71(z0, z1, z2))) → c81(X(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(x(x0, U72(z0, z1, z2))) → c81(X(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(x(x0, x(z0, z1))) → c81(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(x(U11(z0, z1), x1)) → c81(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(x(U12(z0), x1)) → c81(X(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(x(isNat(z0), x1)) → c81(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(x(U21(z0), x1)) → c81(X(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(x(U31(z0, z1), x1)) → c81(X(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(x(U32(z0), x1)) → c81(X(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(x(U41(z0, z1), x1)) → c81(X(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(x(U51(z0, z1, z2), x1)) → c81(X(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(x(U52(z0, z1, z2), x1)) → c81(X(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(x(s(z0), x1)) → c81(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(x(plus(z0, z1), x1)) → c81(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(x(U61(z0), x1)) → c81(X(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(x(U71(z0, z1, z2), x1)) → c81(X(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(x(U72(z0, z1, z2), x1)) → c81(X(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(x(x(z0, z1), x1)) → c81(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(x(x0, tt)) → c81(X(proper(x0), ok(tt)), PROPER(x0))
PROPER(x(x0, 0)) → c81(X(proper(x0), ok(0)), PROPER(x0))
PROPER(x(tt, x1)) → c81(X(ok(tt), proper(x1)), PROPER(x1))
PROPER(x(0, x1)) → c81(X(ok(0), proper(x1)), PROPER(x1))
TOP(mark(U11(z0, z1))) → c83(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
TOP(mark(U12(z0))) → c83(TOP(U12(proper(z0))), PROPER(U12(z0)))
TOP(mark(isNat(z0))) → c83(TOP(isNat(proper(z0))), PROPER(isNat(z0)))
TOP(mark(U21(z0))) → c83(TOP(U21(proper(z0))), PROPER(U21(z0)))
TOP(mark(U31(z0, z1))) → c83(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
TOP(mark(U32(z0))) → c83(TOP(U32(proper(z0))), PROPER(U32(z0)))
TOP(mark(U41(z0, z1))) → c83(TOP(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
TOP(mark(U51(z0, z1, z2))) → c83(TOP(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
TOP(mark(U52(z0, z1, z2))) → c83(TOP(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
TOP(mark(s(z0))) → c83(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(plus(z0, z1))) → c83(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(U61(z0))) → c83(TOP(U61(proper(z0))), PROPER(U61(z0)))
TOP(mark(U71(z0, z1, z2))) → c83(TOP(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
TOP(mark(U72(z0, z1, z2))) → c83(TOP(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
TOP(mark(x(z0, z1))) → c83(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
TOP(mark(tt)) → c83(TOP(ok(tt)))
TOP(mark(0)) → c83(TOP(ok(0)))
TOP(ok(U11(tt, z0))) → c84(TOP(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
TOP(ok(U12(tt))) → c84(TOP(mark(tt)), ACTIVE(U12(tt)))
TOP(ok(U21(tt))) → c84(TOP(mark(tt)), ACTIVE(U21(tt)))
TOP(ok(U31(tt, z0))) → c84(TOP(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
TOP(ok(U32(tt))) → c84(TOP(mark(tt)), ACTIVE(U32(tt)))
TOP(ok(U41(tt, z0))) → c84(TOP(mark(z0)), ACTIVE(U41(tt, z0)))
TOP(ok(U51(tt, z0, z1))) → c84(TOP(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
TOP(ok(U52(tt, z0, z1))) → c84(TOP(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
TOP(ok(U61(tt))) → c84(TOP(mark(0)), ACTIVE(U61(tt)))
TOP(ok(U71(tt, z0, z1))) → c84(TOP(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
TOP(ok(U72(tt, z0, z1))) → c84(TOP(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
TOP(ok(isNat(0))) → c84(TOP(mark(tt)), ACTIVE(isNat(0)))
TOP(ok(isNat(plus(z0, z1)))) → c84(TOP(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
TOP(ok(isNat(s(z0)))) → c84(TOP(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
TOP(ok(isNat(x(z0, z1)))) → c84(TOP(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
TOP(ok(plus(z0, 0))) → c84(TOP(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
TOP(ok(plus(z0, s(z1)))) → c84(TOP(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
TOP(ok(x(z0, 0))) → c84(TOP(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
TOP(ok(x(z0, s(z1)))) → c84(TOP(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
TOP(ok(U11(z0, z1))) → c84(TOP(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
TOP(ok(U12(z0))) → c84(TOP(U12(active(z0))), ACTIVE(U12(z0)))
TOP(ok(U21(z0))) → c84(TOP(U21(active(z0))), ACTIVE(U21(z0)))
TOP(ok(U31(z0, z1))) → c84(TOP(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
TOP(ok(U32(z0))) → c84(TOP(U32(active(z0))), ACTIVE(U32(z0)))
TOP(ok(U41(z0, z1))) → c84(TOP(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
TOP(ok(U51(z0, z1, z2))) → c84(TOP(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
TOP(ok(U52(z0, z1, z2))) → c84(TOP(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
TOP(ok(s(z0))) → c84(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(plus(z0, z1))) → c84(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c84(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(U61(z0))) → c84(TOP(U61(active(z0))), ACTIVE(U61(z0)))
TOP(ok(U71(z0, z1, z2))) → c84(TOP(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
TOP(ok(U72(z0, z1, z2))) → c84(TOP(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
TOP(ok(x(z0, z1))) → c84(TOP(x(active(z0), z1)), ACTIVE(x(z0, z1)))
TOP(ok(x(z0, z1))) → c84(TOP(x(z0, active(z1))), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(x(x0, U11(z0, z1))) → c81(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(x(x0, U12(z0))) → c81(X(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(x(x0, isNat(z0))) → c81(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(x(x0, U21(z0))) → c81(X(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(x(x0, U31(z0, z1))) → c81(X(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(x(x0, U32(z0))) → c81(X(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(x(x0, U41(z0, z1))) → c81(X(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(x(x0, U51(z0, z1, z2))) → c81(X(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(x(x0, U52(z0, z1, z2))) → c81(X(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(x(x0, s(z0))) → c81(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(x(x0, plus(z0, z1))) → c81(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(x(x0, U61(z0))) → c81(X(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(x(x0, U71(z0, z1, z2))) → c81(X(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(x(x0, U72(z0, z1, z2))) → c81(X(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(x(x0, x(z0, z1))) → c81(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(x(U11(z0, z1), x1)) → c81(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(x(U12(z0), x1)) → c81(X(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(x(isNat(z0), x1)) → c81(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(x(U21(z0), x1)) → c81(X(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(x(U31(z0, z1), x1)) → c81(X(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(x(U32(z0), x1)) → c81(X(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(x(U41(z0, z1), x1)) → c81(X(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(x(U51(z0, z1, z2), x1)) → c81(X(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(x(U52(z0, z1, z2), x1)) → c81(X(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(x(s(z0), x1)) → c81(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(x(plus(z0, z1), x1)) → c81(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(x(U61(z0), x1)) → c81(X(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(x(U71(z0, z1, z2), x1)) → c81(X(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(x(U72(z0, z1, z2), x1)) → c81(X(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(x(x(z0, z1), x1)) → c81(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(x(x0, tt)) → c81(X(proper(x0), ok(tt)), PROPER(x0))
PROPER(x(x0, 0)) → c81(X(proper(x0), ok(0)), PROPER(x0))
PROPER(x(tt, x1)) → c81(X(ok(tt), proper(x1)), PROPER(x1))
PROPER(x(0, x1)) → c81(X(ok(0), proper(x1)), PROPER(x1))
TOP(mark(U11(z0, z1))) → c83(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
TOP(mark(U12(z0))) → c83(TOP(U12(proper(z0))), PROPER(U12(z0)))
TOP(mark(isNat(z0))) → c83(TOP(isNat(proper(z0))), PROPER(isNat(z0)))
TOP(mark(U21(z0))) → c83(TOP(U21(proper(z0))), PROPER(U21(z0)))
TOP(mark(U31(z0, z1))) → c83(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
TOP(mark(U32(z0))) → c83(TOP(U32(proper(z0))), PROPER(U32(z0)))
TOP(mark(U41(z0, z1))) → c83(TOP(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
TOP(mark(U51(z0, z1, z2))) → c83(TOP(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
TOP(mark(U52(z0, z1, z2))) → c83(TOP(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
TOP(mark(s(z0))) → c83(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(plus(z0, z1))) → c83(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(U61(z0))) → c83(TOP(U61(proper(z0))), PROPER(U61(z0)))
TOP(mark(U71(z0, z1, z2))) → c83(TOP(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
TOP(mark(U72(z0, z1, z2))) → c83(TOP(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
TOP(mark(x(z0, z1))) → c83(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
TOP(mark(tt)) → c83(TOP(ok(tt)))
TOP(mark(0)) → c83(TOP(ok(0)))
TOP(ok(U11(tt, z0))) → c84(TOP(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
TOP(ok(U12(tt))) → c84(TOP(mark(tt)), ACTIVE(U12(tt)))
TOP(ok(U21(tt))) → c84(TOP(mark(tt)), ACTIVE(U21(tt)))
TOP(ok(U31(tt, z0))) → c84(TOP(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
TOP(ok(U32(tt))) → c84(TOP(mark(tt)), ACTIVE(U32(tt)))
TOP(ok(U41(tt, z0))) → c84(TOP(mark(z0)), ACTIVE(U41(tt, z0)))
TOP(ok(U51(tt, z0, z1))) → c84(TOP(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
TOP(ok(U52(tt, z0, z1))) → c84(TOP(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
TOP(ok(U61(tt))) → c84(TOP(mark(0)), ACTIVE(U61(tt)))
TOP(ok(U71(tt, z0, z1))) → c84(TOP(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
TOP(ok(U72(tt, z0, z1))) → c84(TOP(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
TOP(ok(isNat(0))) → c84(TOP(mark(tt)), ACTIVE(isNat(0)))
TOP(ok(isNat(plus(z0, z1)))) → c84(TOP(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
TOP(ok(isNat(s(z0)))) → c84(TOP(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
TOP(ok(isNat(x(z0, z1)))) → c84(TOP(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
TOP(ok(plus(z0, 0))) → c84(TOP(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
TOP(ok(plus(z0, s(z1)))) → c84(TOP(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
TOP(ok(x(z0, 0))) → c84(TOP(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
TOP(ok(x(z0, s(z1)))) → c84(TOP(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
TOP(ok(U11(z0, z1))) → c84(TOP(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
TOP(ok(U12(z0))) → c84(TOP(U12(active(z0))), ACTIVE(U12(z0)))
TOP(ok(U21(z0))) → c84(TOP(U21(active(z0))), ACTIVE(U21(z0)))
TOP(ok(U31(z0, z1))) → c84(TOP(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
TOP(ok(U32(z0))) → c84(TOP(U32(active(z0))), ACTIVE(U32(z0)))
TOP(ok(U41(z0, z1))) → c84(TOP(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
TOP(ok(U51(z0, z1, z2))) → c84(TOP(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
TOP(ok(U52(z0, z1, z2))) → c84(TOP(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
TOP(ok(s(z0))) → c84(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(plus(z0, z1))) → c84(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c84(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(U61(z0))) → c84(TOP(U61(active(z0))), ACTIVE(U61(z0)))
TOP(ok(U71(z0, z1, z2))) → c84(TOP(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
TOP(ok(U72(z0, z1, z2))) → c84(TOP(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
TOP(ok(x(z0, z1))) → c84(TOP(x(active(z0), z1)), ACTIVE(x(z0, z1)))
TOP(ok(x(z0, z1))) → c84(TOP(x(z0, active(z1))), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT, PROPER, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77, c79, c79, c80, c80, c81, c81, c83, c83, c84
(149) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)
Removed 7 trailing nodes:
TOP(ok(U21(tt))) → c84(TOP(mark(tt)), ACTIVE(U21(tt)))
TOP(ok(isNat(0))) → c84(TOP(mark(tt)), ACTIVE(isNat(0)))
TOP(ok(U32(tt))) → c84(TOP(mark(tt)), ACTIVE(U32(tt)))
TOP(ok(U61(tt))) → c84(TOP(mark(0)), ACTIVE(U61(tt)))
TOP(mark(tt)) → c83(TOP(ok(tt)))
TOP(mark(0)) → c83(TOP(ok(0)))
TOP(ok(U12(tt))) → c84(TOP(mark(tt)), ACTIVE(U12(tt)))
(150) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(x(x0, U11(z0, z1))) → c81(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(x(x0, U12(z0))) → c81(X(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(x(x0, isNat(z0))) → c81(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(x(x0, U21(z0))) → c81(X(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(x(x0, U31(z0, z1))) → c81(X(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(x(x0, U32(z0))) → c81(X(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(x(x0, U41(z0, z1))) → c81(X(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(x(x0, U51(z0, z1, z2))) → c81(X(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(x(x0, U52(z0, z1, z2))) → c81(X(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(x(x0, s(z0))) → c81(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(x(x0, plus(z0, z1))) → c81(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(x(x0, U61(z0))) → c81(X(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(x(x0, U71(z0, z1, z2))) → c81(X(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(x(x0, U72(z0, z1, z2))) → c81(X(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(x(x0, x(z0, z1))) → c81(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(x(U11(z0, z1), x1)) → c81(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(x(U12(z0), x1)) → c81(X(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(x(isNat(z0), x1)) → c81(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(x(U21(z0), x1)) → c81(X(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(x(U31(z0, z1), x1)) → c81(X(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(x(U32(z0), x1)) → c81(X(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(x(U41(z0, z1), x1)) → c81(X(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(x(U51(z0, z1, z2), x1)) → c81(X(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(x(U52(z0, z1, z2), x1)) → c81(X(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(x(s(z0), x1)) → c81(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(x(plus(z0, z1), x1)) → c81(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(x(U61(z0), x1)) → c81(X(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(x(U71(z0, z1, z2), x1)) → c81(X(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(x(U72(z0, z1, z2), x1)) → c81(X(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(x(x(z0, z1), x1)) → c81(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(x(x0, tt)) → c81(X(proper(x0), ok(tt)), PROPER(x0))
PROPER(x(x0, 0)) → c81(X(proper(x0), ok(0)), PROPER(x0))
PROPER(x(tt, x1)) → c81(X(ok(tt), proper(x1)), PROPER(x1))
PROPER(x(0, x1)) → c81(X(ok(0), proper(x1)), PROPER(x1))
TOP(mark(U11(z0, z1))) → c83(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
TOP(mark(U12(z0))) → c83(TOP(U12(proper(z0))), PROPER(U12(z0)))
TOP(mark(isNat(z0))) → c83(TOP(isNat(proper(z0))), PROPER(isNat(z0)))
TOP(mark(U21(z0))) → c83(TOP(U21(proper(z0))), PROPER(U21(z0)))
TOP(mark(U31(z0, z1))) → c83(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
TOP(mark(U32(z0))) → c83(TOP(U32(proper(z0))), PROPER(U32(z0)))
TOP(mark(U41(z0, z1))) → c83(TOP(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
TOP(mark(U51(z0, z1, z2))) → c83(TOP(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
TOP(mark(U52(z0, z1, z2))) → c83(TOP(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
TOP(mark(s(z0))) → c83(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(plus(z0, z1))) → c83(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(U61(z0))) → c83(TOP(U61(proper(z0))), PROPER(U61(z0)))
TOP(mark(U71(z0, z1, z2))) → c83(TOP(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
TOP(mark(U72(z0, z1, z2))) → c83(TOP(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
TOP(mark(x(z0, z1))) → c83(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
TOP(ok(U11(tt, z0))) → c84(TOP(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
TOP(ok(U31(tt, z0))) → c84(TOP(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
TOP(ok(U41(tt, z0))) → c84(TOP(mark(z0)), ACTIVE(U41(tt, z0)))
TOP(ok(U51(tt, z0, z1))) → c84(TOP(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
TOP(ok(U52(tt, z0, z1))) → c84(TOP(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
TOP(ok(U71(tt, z0, z1))) → c84(TOP(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
TOP(ok(U72(tt, z0, z1))) → c84(TOP(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
TOP(ok(isNat(plus(z0, z1)))) → c84(TOP(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
TOP(ok(isNat(s(z0)))) → c84(TOP(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
TOP(ok(isNat(x(z0, z1)))) → c84(TOP(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
TOP(ok(plus(z0, 0))) → c84(TOP(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
TOP(ok(plus(z0, s(z1)))) → c84(TOP(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
TOP(ok(x(z0, 0))) → c84(TOP(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
TOP(ok(x(z0, s(z1)))) → c84(TOP(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
TOP(ok(U11(z0, z1))) → c84(TOP(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
TOP(ok(U12(z0))) → c84(TOP(U12(active(z0))), ACTIVE(U12(z0)))
TOP(ok(U21(z0))) → c84(TOP(U21(active(z0))), ACTIVE(U21(z0)))
TOP(ok(U31(z0, z1))) → c84(TOP(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
TOP(ok(U32(z0))) → c84(TOP(U32(active(z0))), ACTIVE(U32(z0)))
TOP(ok(U41(z0, z1))) → c84(TOP(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
TOP(ok(U51(z0, z1, z2))) → c84(TOP(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
TOP(ok(U52(z0, z1, z2))) → c84(TOP(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
TOP(ok(s(z0))) → c84(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(plus(z0, z1))) → c84(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c84(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(U61(z0))) → c84(TOP(U61(active(z0))), ACTIVE(U61(z0)))
TOP(ok(U71(z0, z1, z2))) → c84(TOP(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
TOP(ok(U72(z0, z1, z2))) → c84(TOP(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
TOP(ok(x(z0, z1))) → c84(TOP(x(active(z0), z1)), ACTIVE(x(z0, z1)))
TOP(ok(x(z0, z1))) → c84(TOP(x(z0, active(z1))), ACTIVE(x(z0, z1)))
S tuples:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(x(x0, U11(z0, z1))) → c81(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(x(x0, U12(z0))) → c81(X(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(x(x0, isNat(z0))) → c81(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(x(x0, U21(z0))) → c81(X(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(x(x0, U31(z0, z1))) → c81(X(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(x(x0, U32(z0))) → c81(X(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(x(x0, U41(z0, z1))) → c81(X(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(x(x0, U51(z0, z1, z2))) → c81(X(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(x(x0, U52(z0, z1, z2))) → c81(X(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(x(x0, s(z0))) → c81(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(x(x0, plus(z0, z1))) → c81(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(x(x0, U61(z0))) → c81(X(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(x(x0, U71(z0, z1, z2))) → c81(X(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(x(x0, U72(z0, z1, z2))) → c81(X(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(x(x0, x(z0, z1))) → c81(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(x(U11(z0, z1), x1)) → c81(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(x(U12(z0), x1)) → c81(X(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(x(isNat(z0), x1)) → c81(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(x(U21(z0), x1)) → c81(X(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(x(U31(z0, z1), x1)) → c81(X(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(x(U32(z0), x1)) → c81(X(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(x(U41(z0, z1), x1)) → c81(X(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(x(U51(z0, z1, z2), x1)) → c81(X(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(x(U52(z0, z1, z2), x1)) → c81(X(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(x(s(z0), x1)) → c81(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(x(plus(z0, z1), x1)) → c81(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(x(U61(z0), x1)) → c81(X(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(x(U71(z0, z1, z2), x1)) → c81(X(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(x(U72(z0, z1, z2), x1)) → c81(X(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(x(x(z0, z1), x1)) → c81(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(x(x0, tt)) → c81(X(proper(x0), ok(tt)), PROPER(x0))
PROPER(x(x0, 0)) → c81(X(proper(x0), ok(0)), PROPER(x0))
PROPER(x(tt, x1)) → c81(X(ok(tt), proper(x1)), PROPER(x1))
PROPER(x(0, x1)) → c81(X(ok(0), proper(x1)), PROPER(x1))
TOP(mark(U11(z0, z1))) → c83(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
TOP(mark(U12(z0))) → c83(TOP(U12(proper(z0))), PROPER(U12(z0)))
TOP(mark(isNat(z0))) → c83(TOP(isNat(proper(z0))), PROPER(isNat(z0)))
TOP(mark(U21(z0))) → c83(TOP(U21(proper(z0))), PROPER(U21(z0)))
TOP(mark(U31(z0, z1))) → c83(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
TOP(mark(U32(z0))) → c83(TOP(U32(proper(z0))), PROPER(U32(z0)))
TOP(mark(U41(z0, z1))) → c83(TOP(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
TOP(mark(U51(z0, z1, z2))) → c83(TOP(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
TOP(mark(U52(z0, z1, z2))) → c83(TOP(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
TOP(mark(s(z0))) → c83(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(plus(z0, z1))) → c83(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(U61(z0))) → c83(TOP(U61(proper(z0))), PROPER(U61(z0)))
TOP(mark(U71(z0, z1, z2))) → c83(TOP(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
TOP(mark(U72(z0, z1, z2))) → c83(TOP(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
TOP(mark(x(z0, z1))) → c83(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
TOP(ok(U11(tt, z0))) → c84(TOP(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
TOP(ok(U31(tt, z0))) → c84(TOP(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
TOP(ok(U41(tt, z0))) → c84(TOP(mark(z0)), ACTIVE(U41(tt, z0)))
TOP(ok(U51(tt, z0, z1))) → c84(TOP(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
TOP(ok(U52(tt, z0, z1))) → c84(TOP(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
TOP(ok(U71(tt, z0, z1))) → c84(TOP(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
TOP(ok(U72(tt, z0, z1))) → c84(TOP(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
TOP(ok(isNat(plus(z0, z1)))) → c84(TOP(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
TOP(ok(isNat(s(z0)))) → c84(TOP(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
TOP(ok(isNat(x(z0, z1)))) → c84(TOP(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
TOP(ok(plus(z0, 0))) → c84(TOP(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
TOP(ok(plus(z0, s(z1)))) → c84(TOP(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
TOP(ok(x(z0, 0))) → c84(TOP(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
TOP(ok(x(z0, s(z1)))) → c84(TOP(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
TOP(ok(U11(z0, z1))) → c84(TOP(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
TOP(ok(U12(z0))) → c84(TOP(U12(active(z0))), ACTIVE(U12(z0)))
TOP(ok(U21(z0))) → c84(TOP(U21(active(z0))), ACTIVE(U21(z0)))
TOP(ok(U31(z0, z1))) → c84(TOP(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
TOP(ok(U32(z0))) → c84(TOP(U32(active(z0))), ACTIVE(U32(z0)))
TOP(ok(U41(z0, z1))) → c84(TOP(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
TOP(ok(U51(z0, z1, z2))) → c84(TOP(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
TOP(ok(U52(z0, z1, z2))) → c84(TOP(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
TOP(ok(s(z0))) → c84(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(plus(z0, z1))) → c84(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c84(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(U61(z0))) → c84(TOP(U61(active(z0))), ACTIVE(U61(z0)))
TOP(ok(U71(z0, z1, z2))) → c84(TOP(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
TOP(ok(U72(z0, z1, z2))) → c84(TOP(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
TOP(ok(x(z0, z1))) → c84(TOP(x(active(z0), z1)), ACTIVE(x(z0, z1)))
TOP(ok(x(z0, z1))) → c84(TOP(x(z0, active(z1))), ACTIVE(x(z0, z1)))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
ACTIVE, U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT, PROPER, TOP
Compound Symbols:
c28, c29, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82, c13, c16, c18, c1, c19, c19, c, c20, c20, c2, c21, c21, c3, c22, c22, c4, c23, c23, c5, c24, c24, c6, c25, c25, c7, c26, c26, c8, c27, c27, c9, c30, c30, c10, c31, c31, c11, c32, c32, c12, c65, c65, c67, c67, c68, c68, c69, c69, c70, c70, c71, c71, c72, c72, c73, c73, c74, c74, c75, c75, c76, c76, c77, c77, c79, c79, c80, c80, c81, c81, c83, c84
(151) CdtUnreachableProof (EQUIVALENT transformation)
The following tuples could be removed as they are not reachable from basic start terms:
ACTIVE(plus(z0, z1)) → c28(PLUS(active(z0), z1), ACTIVE(z0))
ACTIVE(plus(z0, z1)) → c29(PLUS(z0, active(z1)), ACTIVE(z1))
ACTIVE(x(z0, z1)) → c33(X(active(z0), z1), ACTIVE(z0))
ACTIVE(x(z0, z1)) → c34(X(z0, active(z1)), ACTIVE(z1))
ACTIVE(isNat(s(z0))) → c13(ISNAT(z0))
ACTIVE(plus(z0, s(z1))) → c16(ISNAT(z1))
ACTIVE(x(z0, s(z1))) → c18(ISNAT(z1))
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0)))
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U31(tt, z0)) → c1(U32'(isNat(z0)))
ACTIVE(U31(tt, z0)) → c1(ISNAT(z0))
ACTIVE(U51(tt, z0, z1)) → c1(U52'(isNat(z1), z0, z1))
ACTIVE(U51(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U52(tt, z0, z1)) → c1(S(plus(z1, z0)))
ACTIVE(U52(tt, z0, z1)) → c1(PLUS(z1, z0))
ACTIVE(U71(tt, z0, z1)) → c1(U72'(isNat(z1), z0, z1))
ACTIVE(U71(tt, z0, z1)) → c1(ISNAT(z1))
ACTIVE(U72(tt, z0, z1)) → c1(PLUS(x(z1, z0), z1))
ACTIVE(U72(tt, z0, z1)) → c1(X(z1, z0))
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1))
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0))
ACTIVE(isNat(x(z0, z1))) → c1(U31'(isNat(z0), z1))
ACTIVE(isNat(x(z0, z1))) → c1(ISNAT(z0))
ACTIVE(plus(z0, 0)) → c1(U41'(isNat(z0), z0))
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
ACTIVE(x(z0, 0)) → c1(U61'(isNat(z0)))
ACTIVE(x(z0, 0)) → c1(ISNAT(z0))
ACTIVE(U11(plus(z0, 0), x1)) → c19(U11'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U11(plus(z0, s(z1)), x1)) → c19(U11'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U11(x(z0, 0), x1)) → c19(U11'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U11(x(z0, s(z1)), x1)) → c19(U11'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U11(U11(z0, z1), x1)) → c19(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U11(U12(z0), x1)) → c19(U11'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U11(U21(z0), x1)) → c19(U11'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U11(U31(z0, z1), x1)) → c19(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U11(U32(z0), x1)) → c19(U11'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U11(U41(z0, z1), x1)) → c19(U11'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U11(U51(z0, z1, z2), x1)) → c19(U11'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U11(U52(z0, z1, z2), x1)) → c19(U11'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U11(s(z0), x1)) → c19(U11'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(plus(z0, z1), x1)) → c19(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U11(U61(z0), x1)) → c19(U11'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U11(U71(z0, z1, z2), x1)) → c19(U11'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U11(U72(z0, z1, z2), x1)) → c19(U11'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(x(z0, z1), x1)) → c19(U11'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(isNat(0), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1))
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0)))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1))
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(U11'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U11(isNat(x(z0, z1)), x1)) → c(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U12(plus(z0, 0))) → c20(U12'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U12(plus(z0, s(z1)))) → c20(U12'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U12(x(z0, 0))) → c20(U12'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U12(x(z0, s(z1)))) → c20(U12'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U12(U11(z0, z1))) → c20(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U12(U12(z0))) → c20(U12'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U12(U21(z0))) → c20(U12'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U12(U31(z0, z1))) → c20(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U12(U32(z0))) → c20(U12'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U12(U41(z0, z1))) → c20(U12'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U12(U51(z0, z1, z2))) → c20(U12'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U12(U52(z0, z1, z2))) → c20(U12'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U12(s(z0))) → c20(U12'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U12(plus(z0, z1))) → c20(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U12(U61(z0))) → c20(U12'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U12(U71(z0, z1, z2))) → c20(U12'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U12(U72(z0, z1, z2))) → c20(U12'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U12(x(z0, z1))) → c20(U12'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U12(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U12(tt))) → c20(U12'(mark(tt)))
ACTIVE(U12(isNat(0))) → c20(U12'(mark(tt)))
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0)))))
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0)))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1))))
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0)))))
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(U12'(mark(U31(isNat(z0), z1))))
ACTIVE(U12(isNat(x(z0, z1)))) → c2(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U21(plus(z0, 0))) → c21(U21'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U21(plus(z0, s(z1)))) → c21(U21'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U21(x(z0, 0))) → c21(U21'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U21(x(z0, s(z1)))) → c21(U21'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U21(U11(z0, z1))) → c21(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U21(U12(z0))) → c21(U21'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U21(U21(z0))) → c21(U21'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U21(U31(z0, z1))) → c21(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U21(U32(z0))) → c21(U21'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U21(U41(z0, z1))) → c21(U21'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U21(U51(z0, z1, z2))) → c21(U21'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U21(U52(z0, z1, z2))) → c21(U21'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U21(s(z0))) → c21(U21'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U21(plus(z0, z1))) → c21(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U21(U61(z0))) → c21(U21'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U21(U71(z0, z1, z2))) → c21(U21'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U21(U72(z0, z1, z2))) → c21(U21'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U21(x(z0, z1))) → c21(U21'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U21(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U21(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U12(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(U21(tt))) → c21(U21'(mark(tt)))
ACTIVE(U21(isNat(0))) → c21(U21'(mark(tt)))
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0)))))
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0)))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1))))
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0)))))
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(U21'(mark(U31(isNat(z0), z1))))
ACTIVE(U21(isNat(x(z0, z1)))) → c3(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U31(plus(z0, 0), x1)) → c22(U31'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U31(plus(z0, s(z1)), x1)) → c22(U31'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U31(x(z0, 0), x1)) → c22(U31'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U31(x(z0, s(z1)), x1)) → c22(U31'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U31(U11(z0, z1), x1)) → c22(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U31(U12(z0), x1)) → c22(U31'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U31(U21(z0), x1)) → c22(U31'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U31(U31(z0, z1), x1)) → c22(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U31(U32(z0), x1)) → c22(U31'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U31(U41(z0, z1), x1)) → c22(U31'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U31(U51(z0, z1, z2), x1)) → c22(U31'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U31(U52(z0, z1, z2), x1)) → c22(U31'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U31(s(z0), x1)) → c22(U31'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(plus(z0, z1), x1)) → c22(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U31(U61(z0), x1)) → c22(U31'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U31(U71(z0, z1, z2), x1)) → c22(U31'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U31(U72(z0, z1, z2), x1)) → c22(U31'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(x(z0, z1), x1)) → c22(U31'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U31(U12(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(U21(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U31(isNat(0), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(U11'(mark(U32(isNat(z0))), x1))
ACTIVE(U11(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U12(U31(tt, z0))) → c4(U12'(mark(U32(isNat(z0)))))
ACTIVE(U12(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U21(U31(tt, z0))) → c4(U21'(mark(U32(isNat(z0)))))
ACTIVE(U21(U31(tt, z0))) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1))
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0)))
ACTIVE(U31(U31(tt, z0), x1)) → c4(U31'(mark(U32(isNat(z0))), x1))
ACTIVE(U31(U31(tt, z0), x1)) → c4(ACTIVE(U31(tt, z0)))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1))
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(U31'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U31(isNat(x(z0, z1)), x1)) → c4(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U32(plus(z0, 0))) → c23(U32'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U32(plus(z0, s(z1)))) → c23(U32'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U32(x(z0, 0))) → c23(U32'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U32(x(z0, s(z1)))) → c23(U32'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U32(U11(z0, z1))) → c23(U32'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U32(U12(z0))) → c23(U32'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U32(U21(z0))) → c23(U32'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U32(U31(z0, z1))) → c23(U32'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U32(U32(z0))) → c23(U32'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U32(U41(z0, z1))) → c23(U32'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U32(U51(z0, z1, z2))) → c23(U32'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U32(U52(z0, z1, z2))) → c23(U32'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U32(s(z0))) → c23(U32'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U32(plus(z0, z1))) → c23(U32'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U32(U61(z0))) → c23(U32'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U32(U71(z0, z1, z2))) → c23(U32'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U32(U72(z0, z1, z2))) → c23(U32'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U32(x(z0, z1))) → c23(U32'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U32(tt), x1)) → c19(U11'(mark(tt), x1))
ACTIVE(U12(U32(tt))) → c20(U12'(mark(tt)))
ACTIVE(U21(U32(tt))) → c21(U21'(mark(tt)))
ACTIVE(U31(U32(tt), x1)) → c22(U31'(mark(tt), x1))
ACTIVE(U32(U12(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U21(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(U32(tt))) → c23(U32'(mark(tt)))
ACTIVE(U32(isNat(0))) → c23(U32'(mark(tt)))
ACTIVE(U32(U11(tt, z0))) → c5(U32'(mark(U12(isNat(z0)))))
ACTIVE(U32(U11(tt, z0))) → c5(ACTIVE(U11(tt, z0)))
ACTIVE(U32(U31(tt, z0))) → c5(U32'(mark(U32(isNat(z0)))))
ACTIVE(U32(U31(tt, z0))) → c5(ACTIVE(U31(tt, z0)))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(U32'(mark(U11(isNat(z0), z1))))
ACTIVE(U32(isNat(plus(z0, z1)))) → c5(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U32(isNat(s(z0)))) → c5(U32'(mark(U21(isNat(z0)))))
ACTIVE(U32(isNat(s(z0)))) → c5(ACTIVE(isNat(s(z0))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(U32'(mark(U31(isNat(z0), z1))))
ACTIVE(U32(isNat(x(z0, z1)))) → c5(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U41(plus(z0, 0), x1)) → c24(U41'(mark(U41(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0)))
ACTIVE(U41(plus(z0, s(z1)), x1)) → c24(U41'(mark(U51(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1))))
ACTIVE(U41(x(z0, 0), x1)) → c24(U41'(mark(U61(isNat(z0))), x1), ACTIVE(x(z0, 0)))
ACTIVE(U41(x(z0, s(z1)), x1)) → c24(U41'(mark(U71(isNat(z1), z1, z0)), x1), ACTIVE(x(z0, s(z1))))
ACTIVE(U41(U11(z0, z1), x1)) → c24(U41'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1)))
ACTIVE(U41(U12(z0), x1)) → c24(U41'(U12(active(z0)), x1), ACTIVE(U12(z0)))
ACTIVE(U41(U21(z0), x1)) → c24(U41'(U21(active(z0)), x1), ACTIVE(U21(z0)))
ACTIVE(U41(U31(z0, z1), x1)) → c24(U41'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1)))
ACTIVE(U41(U32(z0), x1)) → c24(U41'(U32(active(z0)), x1), ACTIVE(U32(z0)))
ACTIVE(U41(U41(z0, z1), x1)) → c24(U41'(U41(active(z0), z1), x1), ACTIVE(U41(z0, z1)))
ACTIVE(U41(U51(z0, z1, z2), x1)) → c24(U41'(U51(active(z0), z1, z2), x1), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U41(U52(z0, z1, z2), x1)) → c24(U41'(U52(active(z0), z1, z2), x1), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U41(s(z0), x1)) → c24(U41'(s(active(z0)), x1), ACTIVE(s(z0)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(plus(z0, z1), x1)) → c24(U41'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
ACTIVE(U41(U61(z0), x1)) → c24(U41'(U61(active(z0)), x1), ACTIVE(U61(z0)))
ACTIVE(U41(U71(z0, z1, z2), x1)) → c24(U41'(U71(active(z0), z1, z2), x1), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U41(U72(z0, z1, z2), x1)) → c24(U41'(U72(active(z0), z1, z2), x1), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(active(z0), z1), x1), ACTIVE(x(z0, z1)))
ACTIVE(U41(x(z0, z1), x1)) → c24(U41'(x(z0, active(z1)), x1), ACTIVE(x(z0, z1)))
ACTIVE(U11(U41(tt, z0), x1)) → c19(U11'(mark(z0), x1))
ACTIVE(U12(U41(tt, z0))) → c20(U12'(mark(z0)))
ACTIVE(U21(U41(tt, z0))) → c21(U21'(mark(z0)))
ACTIVE(U31(U41(tt, z0), x1)) → c22(U31'(mark(z0), x1))
ACTIVE(U32(U41(tt, z0))) → c23(U32'(mark(z0)))
ACTIVE(U41(U12(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U21(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U32(tt), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U41(tt, z0), x1)) → c24(U41'(mark(z0), x1))
ACTIVE(U41(isNat(0), x1)) → c24(U41'(mark(tt), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(U41'(mark(U12(isNat(z0))), x1))
ACTIVE(U41(U11(tt, z0), x1)) → c6(ACTIVE(U11(tt, z0)))
ACTIVE(U41(U31(tt, z0), x1)) → c6(U41'(mark(U32(isNat(z0))), x1))
ACTIVE(U41(U31(tt, z0), x1)) → c6(ACTIVE(U31(tt, z0)))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(U41'(mark(U11(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(plus(z0, z1)), x1)) → c6(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(U41'(mark(U21(isNat(z0))), x1))
ACTIVE(U41(isNat(s(z0)), x1)) → c6(ACTIVE(isNat(s(z0))))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(U41'(mark(U31(isNat(z0), z1)), x1))
ACTIVE(U41(isNat(x(z0, z1)), x1)) → c6(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U51(plus(z0, 0), x1, x2)) → c25(U51'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U51(plus(z0, s(z1)), x1, x2)) → c25(U51'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U51(x(z0, 0), x1, x2)) → c25(U51'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U51(x(z0, s(z1)), x1, x2)) → c25(U51'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U51(U11(z0, z1), x1, x2)) → c25(U51'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U51(U12(z0), x1, x2)) → c25(U51'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U51(U21(z0), x1, x2)) → c25(U51'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U51(U31(z0, z1), x1, x2)) → c25(U51'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U51(U32(z0), x1, x2)) → c25(U51'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U51(U41(z0, z1), x1, x2)) → c25(U51'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U51(U51(z0, z1, z2), x1, x2)) → c25(U51'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U51(U52(z0, z1, z2), x1, x2)) → c25(U51'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U51(s(z0), x1, x2)) → c25(U51'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(plus(z0, z1), x1, x2)) → c25(U51'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U51(U61(z0), x1, x2)) → c25(U51'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U51(U71(z0, z1, z2), x1, x2)) → c25(U51'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U51(U72(z0, z1, z2), x1, x2)) → c25(U51'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(x(z0, z1), x1, x2)) → c25(U51'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U51(U12(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U21(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U32(tt), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U51(U41(tt, z0), x1, x2)) → c25(U51'(mark(z0), x1, x2))
ACTIVE(U51(isNat(0), x1, x2)) → c25(U51'(mark(tt), x1, x2))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(U11'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U12(U51(tt, z0, z1))) → c7(U12'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U12(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U21(U51(tt, z0, z1))) → c7(U21'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U21(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(U31'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U32(U51(tt, z0, z1))) → c7(U32'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U32(U51(tt, z0, z1))) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(U41'(mark(U52(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U51(tt, z0, z1), x1)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(U51'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U51(U11(tt, z0), x1, x2)) → c7(ACTIVE(U11(tt, z0)))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(U51'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U51(U31(tt, z0), x1, x2)) → c7(ACTIVE(U31(tt, z0)))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(U51'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U51(tt, z0, z1), x1, x2)) → c7(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(U51'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(plus(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(U51'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U51(isNat(s(z0)), x1, x2)) → c7(ACTIVE(isNat(s(z0))))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(U51'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U51(isNat(x(z0, z1)), x1, x2)) → c7(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U52(plus(z0, 0), x1, x2)) → c26(U52'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U52(plus(z0, s(z1)), x1, x2)) → c26(U52'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U52(x(z0, 0), x1, x2)) → c26(U52'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U52(x(z0, s(z1)), x1, x2)) → c26(U52'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U52(U11(z0, z1), x1, x2)) → c26(U52'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U52(U12(z0), x1, x2)) → c26(U52'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U52(U21(z0), x1, x2)) → c26(U52'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U52(U31(z0, z1), x1, x2)) → c26(U52'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U52(U32(z0), x1, x2)) → c26(U52'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U52(U41(z0, z1), x1, x2)) → c26(U52'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U52(U51(z0, z1, z2), x1, x2)) → c26(U52'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U52(U52(z0, z1, z2), x1, x2)) → c26(U52'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U52(s(z0), x1, x2)) → c26(U52'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(plus(z0, z1), x1, x2)) → c26(U52'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U52(U61(z0), x1, x2)) → c26(U52'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U52(U71(z0, z1, z2), x1, x2)) → c26(U52'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U52(U72(z0, z1, z2), x1, x2)) → c26(U52'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(x(z0, z1), x1, x2)) → c26(U52'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U52(U12(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U21(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U32(tt), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U52(U41(tt, z0), x1, x2)) → c26(U52'(mark(z0), x1, x2))
ACTIVE(U52(isNat(0), x1, x2)) → c26(U52'(mark(tt), x1, x2))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(U11'(mark(s(plus(z1, z0))), x1))
ACTIVE(U11(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U12(U52(tt, z0, z1))) → c8(U12'(mark(s(plus(z1, z0)))))
ACTIVE(U12(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U21(U52(tt, z0, z1))) → c8(U21'(mark(s(plus(z1, z0)))))
ACTIVE(U21(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(U31'(mark(s(plus(z1, z0))), x1))
ACTIVE(U31(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U32(U52(tt, z0, z1))) → c8(U32'(mark(s(plus(z1, z0)))))
ACTIVE(U32(U52(tt, z0, z1))) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(U41'(mark(s(plus(z1, z0))), x1))
ACTIVE(U41(U52(tt, z0, z1), x1)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(U51'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U51(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(U52'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U52(U11(tt, z0), x1, x2)) → c8(ACTIVE(U11(tt, z0)))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(U52'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U52(U31(tt, z0), x1, x2)) → c8(ACTIVE(U31(tt, z0)))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(U52'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U51(tt, z0, z1), x1, x2)) → c8(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(U52'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U52(U52(tt, z0, z1), x1, x2)) → c8(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(U52'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(plus(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(U52'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U52(isNat(s(z0)), x1, x2)) → c8(ACTIVE(isNat(s(z0))))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(U52'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U52(isNat(x(z0, z1)), x1, x2)) → c8(ACTIVE(isNat(x(z0, z1))))
ACTIVE(s(plus(z0, 0))) → c27(S(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(s(plus(z0, s(z1)))) → c27(S(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(s(x(z0, 0))) → c27(S(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(s(x(z0, s(z1)))) → c27(S(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(s(U11(z0, z1))) → c27(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(s(U12(z0))) → c27(S(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(s(U21(z0))) → c27(S(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(s(U31(z0, z1))) → c27(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(s(U32(z0))) → c27(S(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(s(U41(z0, z1))) → c27(S(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(s(U51(z0, z1, z2))) → c27(S(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(s(U52(z0, z1, z2))) → c27(S(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(s(s(z0))) → c27(S(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(s(plus(z0, z1))) → c27(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(s(U61(z0))) → c27(S(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(s(U71(z0, z1, z2))) → c27(S(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(s(U72(z0, z1, z2))) → c27(S(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(s(x(z0, z1))) → c27(S(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(s(x(z0, z1))) → c27(S(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(s(U12(tt))) → c27(S(mark(tt)))
ACTIVE(s(U21(tt))) → c27(S(mark(tt)))
ACTIVE(s(U32(tt))) → c27(S(mark(tt)))
ACTIVE(s(U41(tt, z0))) → c27(S(mark(z0)))
ACTIVE(s(isNat(0))) → c27(S(mark(tt)))
ACTIVE(s(U11(tt, z0))) → c9(S(mark(U12(isNat(z0)))))
ACTIVE(s(U11(tt, z0))) → c9(ACTIVE(U11(tt, z0)))
ACTIVE(s(U31(tt, z0))) → c9(S(mark(U32(isNat(z0)))))
ACTIVE(s(U31(tt, z0))) → c9(ACTIVE(U31(tt, z0)))
ACTIVE(s(U51(tt, z0, z1))) → c9(S(mark(U52(isNat(z1), z0, z1))))
ACTIVE(s(U51(tt, z0, z1))) → c9(ACTIVE(U51(tt, z0, z1)))
ACTIVE(s(U52(tt, z0, z1))) → c9(S(mark(s(plus(z1, z0)))))
ACTIVE(s(U52(tt, z0, z1))) → c9(ACTIVE(U52(tt, z0, z1)))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(S(mark(U11(isNat(z0), z1))))
ACTIVE(s(isNat(plus(z0, z1)))) → c9(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(s(isNat(s(z0)))) → c9(S(mark(U21(isNat(z0)))))
ACTIVE(s(isNat(s(z0)))) → c9(ACTIVE(isNat(s(z0))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(S(mark(U31(isNat(z0), z1))))
ACTIVE(s(isNat(x(z0, z1)))) → c9(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U61(plus(z0, 0))) → c30(U61'(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
ACTIVE(U61(plus(z0, s(z1)))) → c30(U61'(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
ACTIVE(U61(x(z0, 0))) → c30(U61'(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
ACTIVE(U61(x(z0, s(z1)))) → c30(U61'(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
ACTIVE(U61(U11(z0, z1))) → c30(U61'(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
ACTIVE(U61(U12(z0))) → c30(U61'(U12(active(z0))), ACTIVE(U12(z0)))
ACTIVE(U61(U21(z0))) → c30(U61'(U21(active(z0))), ACTIVE(U21(z0)))
ACTIVE(U61(U31(z0, z1))) → c30(U61'(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
ACTIVE(U61(U32(z0))) → c30(U61'(U32(active(z0))), ACTIVE(U32(z0)))
ACTIVE(U61(U41(z0, z1))) → c30(U61'(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
ACTIVE(U61(U51(z0, z1, z2))) → c30(U61'(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U61(U52(z0, z1, z2))) → c30(U61'(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U61(s(z0))) → c30(U61'(s(active(z0))), ACTIVE(s(z0)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
ACTIVE(U61(plus(z0, z1))) → c30(U61'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
ACTIVE(U61(U61(z0))) → c30(U61'(U61(active(z0))), ACTIVE(U61(z0)))
ACTIVE(U61(U71(z0, z1, z2))) → c30(U61'(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U61(U72(z0, z1, z2))) → c30(U61'(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(active(z0), z1)), ACTIVE(x(z0, z1)))
ACTIVE(U61(x(z0, z1))) → c30(U61'(x(z0, active(z1))), ACTIVE(x(z0, z1)))
ACTIVE(U11(U61(tt), x1)) → c19(U11'(mark(0), x1))
ACTIVE(U12(U61(tt))) → c20(U12'(mark(0)))
ACTIVE(U21(U61(tt))) → c21(U21'(mark(0)))
ACTIVE(U31(U61(tt), x1)) → c22(U31'(mark(0), x1))
ACTIVE(U32(U61(tt))) → c23(U32'(mark(0)))
ACTIVE(U41(U61(tt), x1)) → c24(U41'(mark(0), x1))
ACTIVE(U51(U61(tt), x1, x2)) → c25(U51'(mark(0), x1, x2))
ACTIVE(U52(U61(tt), x1, x2)) → c26(U52'(mark(0), x1, x2))
ACTIVE(s(U61(tt))) → c27(S(mark(0)))
ACTIVE(U61(U12(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U21(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U32(tt))) → c30(U61'(mark(tt)))
ACTIVE(U61(U41(tt, z0))) → c30(U61'(mark(z0)))
ACTIVE(U61(U61(tt))) → c30(U61'(mark(0)))
ACTIVE(U61(isNat(0))) → c30(U61'(mark(tt)))
ACTIVE(U61(U11(tt, z0))) → c10(U61'(mark(U12(isNat(z0)))))
ACTIVE(U61(U11(tt, z0))) → c10(ACTIVE(U11(tt, z0)))
ACTIVE(U61(U31(tt, z0))) → c10(U61'(mark(U32(isNat(z0)))))
ACTIVE(U61(U31(tt, z0))) → c10(ACTIVE(U31(tt, z0)))
ACTIVE(U61(U51(tt, z0, z1))) → c10(U61'(mark(U52(isNat(z1), z0, z1))))
ACTIVE(U61(U51(tt, z0, z1))) → c10(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U61(U52(tt, z0, z1))) → c10(U61'(mark(s(plus(z1, z0)))))
ACTIVE(U61(U52(tt, z0, z1))) → c10(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(U61'(mark(U11(isNat(z0), z1))))
ACTIVE(U61(isNat(plus(z0, z1)))) → c10(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U61(isNat(s(z0)))) → c10(U61'(mark(U21(isNat(z0)))))
ACTIVE(U61(isNat(s(z0)))) → c10(ACTIVE(isNat(s(z0))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(U61'(mark(U31(isNat(z0), z1))))
ACTIVE(U61(isNat(x(z0, z1)))) → c10(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U71(plus(z0, 0), x1, x2)) → c31(U71'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U71(plus(z0, s(z1)), x1, x2)) → c31(U71'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U71(x(z0, 0), x1, x2)) → c31(U71'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U71(x(z0, s(z1)), x1, x2)) → c31(U71'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U71(U11(z0, z1), x1, x2)) → c31(U71'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U71(U12(z0), x1, x2)) → c31(U71'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U71(U21(z0), x1, x2)) → c31(U71'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U71(U31(z0, z1), x1, x2)) → c31(U71'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U71(U32(z0), x1, x2)) → c31(U71'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U71(U41(z0, z1), x1, x2)) → c31(U71'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U71(U51(z0, z1, z2), x1, x2)) → c31(U71'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U71(U52(z0, z1, z2), x1, x2)) → c31(U71'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U71(s(z0), x1, x2)) → c31(U71'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(plus(z0, z1), x1, x2)) → c31(U71'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U71(U61(z0), x1, x2)) → c31(U71'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U71(U71(z0, z1, z2), x1, x2)) → c31(U71'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U71(U72(z0, z1, z2), x1, x2)) → c31(U71'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(x(z0, z1), x1, x2)) → c31(U71'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U71(U12(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U21(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U32(tt), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U71(U41(tt, z0), x1, x2)) → c31(U71'(mark(z0), x1, x2))
ACTIVE(U71(U61(tt), x1, x2)) → c31(U71'(mark(0), x1, x2))
ACTIVE(U71(isNat(0), x1, x2)) → c31(U71'(mark(tt), x1, x2))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(U11'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U11(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U12(U71(tt, z0, z1))) → c11(U12'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U12(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U21(U71(tt, z0, z1))) → c11(U21'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U21(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(U31'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U31(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U32(U71(tt, z0, z1))) → c11(U32'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U32(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(U41'(mark(U72(isNat(z1), z0, z1)), x1))
ACTIVE(U41(U71(tt, z0, z1), x1)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(U51'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U51(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(U52'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U52(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(s(U71(tt, z0, z1))) → c11(S(mark(U72(isNat(z1), z0, z1))))
ACTIVE(s(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U61(U71(tt, z0, z1))) → c11(U61'(mark(U72(isNat(z1), z0, z1))))
ACTIVE(U61(U71(tt, z0, z1))) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(U71'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U71(U11(tt, z0), x1, x2)) → c11(ACTIVE(U11(tt, z0)))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(U71'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U71(U31(tt, z0), x1, x2)) → c11(ACTIVE(U31(tt, z0)))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(U71'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U51(tt, z0, z1), x1, x2)) → c11(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(U71'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U71(U52(tt, z0, z1), x1, x2)) → c11(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(U71'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U71(U71(tt, z0, z1), x1, x2)) → c11(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(U71'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(plus(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(U71'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U71(isNat(s(z0)), x1, x2)) → c11(ACTIVE(isNat(s(z0))))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(U71'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U71(isNat(x(z0, z1)), x1, x2)) → c11(ACTIVE(isNat(x(z0, z1))))
ACTIVE(U72(plus(z0, 0), x1, x2)) → c32(U72'(mark(U41(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0)))
ACTIVE(U72(plus(z0, s(z1)), x1, x2)) → c32(U72'(mark(U51(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1))))
ACTIVE(U72(x(z0, 0), x1, x2)) → c32(U72'(mark(U61(isNat(z0))), x1, x2), ACTIVE(x(z0, 0)))
ACTIVE(U72(x(z0, s(z1)), x1, x2)) → c32(U72'(mark(U71(isNat(z1), z1, z0)), x1, x2), ACTIVE(x(z0, s(z1))))
ACTIVE(U72(U11(z0, z1), x1, x2)) → c32(U72'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1)))
ACTIVE(U72(U12(z0), x1, x2)) → c32(U72'(U12(active(z0)), x1, x2), ACTIVE(U12(z0)))
ACTIVE(U72(U21(z0), x1, x2)) → c32(U72'(U21(active(z0)), x1, x2), ACTIVE(U21(z0)))
ACTIVE(U72(U31(z0, z1), x1, x2)) → c32(U72'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1)))
ACTIVE(U72(U32(z0), x1, x2)) → c32(U72'(U32(active(z0)), x1, x2), ACTIVE(U32(z0)))
ACTIVE(U72(U41(z0, z1), x1, x2)) → c32(U72'(U41(active(z0), z1), x1, x2), ACTIVE(U41(z0, z1)))
ACTIVE(U72(U51(z0, z1, z2), x1, x2)) → c32(U72'(U51(active(z0), z1, z2), x1, x2), ACTIVE(U51(z0, z1, z2)))
ACTIVE(U72(U52(z0, z1, z2), x1, x2)) → c32(U72'(U52(active(z0), z1, z2), x1, x2), ACTIVE(U52(z0, z1, z2)))
ACTIVE(U72(s(z0), x1, x2)) → c32(U72'(s(active(z0)), x1, x2), ACTIVE(s(z0)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(plus(z0, z1), x1, x2)) → c32(U72'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
ACTIVE(U72(U61(z0), x1, x2)) → c32(U72'(U61(active(z0)), x1, x2), ACTIVE(U61(z0)))
ACTIVE(U72(U71(z0, z1, z2), x1, x2)) → c32(U72'(U71(active(z0), z1, z2), x1, x2), ACTIVE(U71(z0, z1, z2)))
ACTIVE(U72(U72(z0, z1, z2), x1, x2)) → c32(U72'(U72(active(z0), z1, z2), x1, x2), ACTIVE(U72(z0, z1, z2)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(active(z0), z1), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(x(z0, z1), x1, x2)) → c32(U72'(x(z0, active(z1)), x1, x2), ACTIVE(x(z0, z1)))
ACTIVE(U72(U12(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U21(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U32(tt), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U72(U41(tt, z0), x1, x2)) → c32(U72'(mark(z0), x1, x2))
ACTIVE(U72(U61(tt), x1, x2)) → c32(U72'(mark(0), x1, x2))
ACTIVE(U72(isNat(0), x1, x2)) → c32(U72'(mark(tt), x1, x2))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(U11'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U11(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U12(U72(tt, z0, z1))) → c12(U12'(mark(plus(x(z1, z0), z1))))
ACTIVE(U12(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U21(U72(tt, z0, z1))) → c12(U21'(mark(plus(x(z1, z0), z1))))
ACTIVE(U21(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(U31'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U31(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U32(U72(tt, z0, z1))) → c12(U32'(mark(plus(x(z1, z0), z1))))
ACTIVE(U32(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(U41'(mark(plus(x(z1, z0), z1)), x1))
ACTIVE(U41(U72(tt, z0, z1), x1)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(U51'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U51(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(U52'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U52(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(s(U72(tt, z0, z1))) → c12(S(mark(plus(x(z1, z0), z1))))
ACTIVE(s(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U61(U72(tt, z0, z1))) → c12(U61'(mark(plus(x(z1, z0), z1))))
ACTIVE(U61(U72(tt, z0, z1))) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(U71'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U71(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(U72'(mark(U12(isNat(z0))), x1, x2))
ACTIVE(U72(U11(tt, z0), x1, x2)) → c12(ACTIVE(U11(tt, z0)))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(U72'(mark(U32(isNat(z0))), x1, x2))
ACTIVE(U72(U31(tt, z0), x1, x2)) → c12(ACTIVE(U31(tt, z0)))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(U72'(mark(U52(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U51(tt, z0, z1), x1, x2)) → c12(ACTIVE(U51(tt, z0, z1)))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(U72'(mark(s(plus(z1, z0))), x1, x2))
ACTIVE(U72(U52(tt, z0, z1), x1, x2)) → c12(ACTIVE(U52(tt, z0, z1)))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(U72'(mark(U72(isNat(z1), z0, z1)), x1, x2))
ACTIVE(U72(U71(tt, z0, z1), x1, x2)) → c12(ACTIVE(U71(tt, z0, z1)))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(U72'(mark(plus(x(z1, z0), z1)), x1, x2))
ACTIVE(U72(U72(tt, z0, z1), x1, x2)) → c12(ACTIVE(U72(tt, z0, z1)))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(U72'(mark(U11(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(plus(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(plus(z0, z1))))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(U72'(mark(U21(isNat(z0))), x1, x2))
ACTIVE(U72(isNat(s(z0)), x1, x2)) → c12(ACTIVE(isNat(s(z0))))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(U72'(mark(U31(isNat(z0), z1)), x1, x2))
ACTIVE(U72(isNat(x(z0, z1)), x1, x2)) → c12(ACTIVE(isNat(x(z0, z1))))
PROPER(U11(x0, U11(z0, z1))) → c65(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U11(x0, U12(z0))) → c65(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U11(x0, isNat(z0))) → c65(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U11(x0, U21(z0))) → c65(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U11(x0, U31(z0, z1))) → c65(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U11(x0, U32(z0))) → c65(U11'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U11(x0, U41(z0, z1))) → c65(U11'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U11(x0, U51(z0, z1, z2))) → c65(U11'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U11(x0, U52(z0, z1, z2))) → c65(U11'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U11(x0, s(z0))) → c65(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U11(x0, plus(z0, z1))) → c65(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U11(x0, U61(z0))) → c65(U11'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U11(x0, U71(z0, z1, z2))) → c65(U11'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U11(x0, U72(z0, z1, z2))) → c65(U11'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U11(x0, x(z0, z1))) → c65(U11'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U11(U11(z0, z1), x1)) → c65(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U11(U12(z0), x1)) → c65(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U11(isNat(z0), x1)) → c65(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U11(U21(z0), x1)) → c65(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U11(U31(z0, z1), x1)) → c65(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U11(U32(z0), x1)) → c65(U11'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U11(U41(z0, z1), x1)) → c65(U11'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U11(U51(z0, z1, z2), x1)) → c65(U11'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U11(U52(z0, z1, z2), x1)) → c65(U11'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U11(s(z0), x1)) → c65(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U11(plus(z0, z1), x1)) → c65(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U11(U61(z0), x1)) → c65(U11'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U11(U71(z0, z1, z2), x1)) → c65(U11'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U11(U72(z0, z1, z2), x1)) → c65(U11'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U11(x(z0, z1), x1)) → c65(U11'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U11(x0, tt)) → c65(U11'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U11(x0, 0)) → c65(U11'(proper(x0), ok(0)), PROPER(x0))
PROPER(U11(tt, x1)) → c65(U11'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U11(0, x1)) → c65(U11'(ok(0), proper(x1)), PROPER(x1))
PROPER(U12(U11(z0, z1))) → c67(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U12(U12(z0))) → c67(U12'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U12(isNat(z0))) → c67(U12'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U12(U21(z0))) → c67(U12'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U12(U31(z0, z1))) → c67(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U12(U32(z0))) → c67(U12'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U12(U41(z0, z1))) → c67(U12'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U12(U51(z0, z1, z2))) → c67(U12'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U12(U52(z0, z1, z2))) → c67(U12'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U12(s(z0))) → c67(U12'(s(proper(z0))), PROPER(s(z0)))
PROPER(U12(plus(z0, z1))) → c67(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U12(U61(z0))) → c67(U12'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U12(U71(z0, z1, z2))) → c67(U12'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U12(U72(z0, z1, z2))) → c67(U12'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U12(x(z0, z1))) → c67(U12'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U12(tt)) → c67(U12'(ok(tt)))
PROPER(U12(0)) → c67(U12'(ok(0)))
PROPER(isNat(U11(z0, z1))) → c68(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(isNat(U12(z0))) → c68(ISNAT(U12(proper(z0))), PROPER(U12(z0)))
PROPER(isNat(isNat(z0))) → c68(ISNAT(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(isNat(U21(z0))) → c68(ISNAT(U21(proper(z0))), PROPER(U21(z0)))
PROPER(isNat(U31(z0, z1))) → c68(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(isNat(U32(z0))) → c68(ISNAT(U32(proper(z0))), PROPER(U32(z0)))
PROPER(isNat(U41(z0, z1))) → c68(ISNAT(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(isNat(U51(z0, z1, z2))) → c68(ISNAT(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(isNat(U52(z0, z1, z2))) → c68(ISNAT(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(isNat(s(z0))) → c68(ISNAT(s(proper(z0))), PROPER(s(z0)))
PROPER(isNat(plus(z0, z1))) → c68(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(isNat(U61(z0))) → c68(ISNAT(U61(proper(z0))), PROPER(U61(z0)))
PROPER(isNat(U71(z0, z1, z2))) → c68(ISNAT(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(isNat(U72(z0, z1, z2))) → c68(ISNAT(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(isNat(x(z0, z1))) → c68(ISNAT(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(isNat(tt)) → c68(ISNAT(ok(tt)))
PROPER(isNat(0)) → c68(ISNAT(ok(0)))
PROPER(U21(U11(z0, z1))) → c69(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U21(U12(z0))) → c69(U21'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U21(isNat(z0))) → c69(U21'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U21(U21(z0))) → c69(U21'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U21(U31(z0, z1))) → c69(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U21(U32(z0))) → c69(U21'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U21(U41(z0, z1))) → c69(U21'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U21(U51(z0, z1, z2))) → c69(U21'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U21(U52(z0, z1, z2))) → c69(U21'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U21(s(z0))) → c69(U21'(s(proper(z0))), PROPER(s(z0)))
PROPER(U21(plus(z0, z1))) → c69(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U21(U61(z0))) → c69(U21'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U21(U71(z0, z1, z2))) → c69(U21'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U21(U72(z0, z1, z2))) → c69(U21'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U21(x(z0, z1))) → c69(U21'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U21(tt)) → c69(U21'(ok(tt)))
PROPER(U21(0)) → c69(U21'(ok(0)))
PROPER(U31(x0, U11(z0, z1))) → c70(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U31(x0, U12(z0))) → c70(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U31(x0, isNat(z0))) → c70(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U31(x0, U21(z0))) → c70(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U31(x0, U31(z0, z1))) → c70(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U31(x0, U32(z0))) → c70(U31'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U31(x0, U41(z0, z1))) → c70(U31'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U31(x0, U51(z0, z1, z2))) → c70(U31'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U31(x0, U52(z0, z1, z2))) → c70(U31'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U31(x0, s(z0))) → c70(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U31(x0, plus(z0, z1))) → c70(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U31(x0, U61(z0))) → c70(U31'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U31(x0, U71(z0, z1, z2))) → c70(U31'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U31(x0, U72(z0, z1, z2))) → c70(U31'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U31(x0, x(z0, z1))) → c70(U31'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U31(U11(z0, z1), x1)) → c70(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U31(U12(z0), x1)) → c70(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U31(isNat(z0), x1)) → c70(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U31(U21(z0), x1)) → c70(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U31(U31(z0, z1), x1)) → c70(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U31(U32(z0), x1)) → c70(U31'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U31(U41(z0, z1), x1)) → c70(U31'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U31(U51(z0, z1, z2), x1)) → c70(U31'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U31(U52(z0, z1, z2), x1)) → c70(U31'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U31(s(z0), x1)) → c70(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U31(plus(z0, z1), x1)) → c70(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U31(U61(z0), x1)) → c70(U31'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U31(U71(z0, z1, z2), x1)) → c70(U31'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U31(U72(z0, z1, z2), x1)) → c70(U31'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U31(x(z0, z1), x1)) → c70(U31'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U31(x0, tt)) → c70(U31'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U31(x0, 0)) → c70(U31'(proper(x0), ok(0)), PROPER(x0))
PROPER(U31(tt, x1)) → c70(U31'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U31(0, x1)) → c70(U31'(ok(0), proper(x1)), PROPER(x1))
PROPER(U32(U11(z0, z1))) → c71(U32'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U32(U12(z0))) → c71(U32'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U32(isNat(z0))) → c71(U32'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U32(U21(z0))) → c71(U32'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U32(U31(z0, z1))) → c71(U32'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U32(U32(z0))) → c71(U32'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U32(U41(z0, z1))) → c71(U32'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U32(U51(z0, z1, z2))) → c71(U32'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U32(U52(z0, z1, z2))) → c71(U32'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U32(s(z0))) → c71(U32'(s(proper(z0))), PROPER(s(z0)))
PROPER(U32(plus(z0, z1))) → c71(U32'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U32(U61(z0))) → c71(U32'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U32(U71(z0, z1, z2))) → c71(U32'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U32(U72(z0, z1, z2))) → c71(U32'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U32(x(z0, z1))) → c71(U32'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U32(tt)) → c71(U32'(ok(tt)))
PROPER(U32(0)) → c71(U32'(ok(0)))
PROPER(U41(x0, U11(z0, z1))) → c72(U41'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(U41(x0, U12(z0))) → c72(U41'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(U41(x0, isNat(z0))) → c72(U41'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(U41(x0, U21(z0))) → c72(U41'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(U41(x0, U31(z0, z1))) → c72(U41'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(U41(x0, U32(z0))) → c72(U41'(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(U41(x0, U41(z0, z1))) → c72(U41'(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(U41(x0, U51(z0, z1, z2))) → c72(U41'(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(U41(x0, U52(z0, z1, z2))) → c72(U41'(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(U41(x0, s(z0))) → c72(U41'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(U41(x0, plus(z0, z1))) → c72(U41'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(U41(x0, U61(z0))) → c72(U41'(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(U41(x0, U71(z0, z1, z2))) → c72(U41'(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(U41(x0, U72(z0, z1, z2))) → c72(U41'(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(U41(x0, x(z0, z1))) → c72(U41'(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(U41(U11(z0, z1), x1)) → c72(U41'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(U41(U12(z0), x1)) → c72(U41'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(U41(isNat(z0), x1)) → c72(U41'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(U41(U21(z0), x1)) → c72(U41'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(U41(U31(z0, z1), x1)) → c72(U41'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(U41(U32(z0), x1)) → c72(U41'(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(U41(U41(z0, z1), x1)) → c72(U41'(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(U41(U51(z0, z1, z2), x1)) → c72(U41'(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(U41(U52(z0, z1, z2), x1)) → c72(U41'(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(U41(s(z0), x1)) → c72(U41'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(U41(plus(z0, z1), x1)) → c72(U41'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(U41(U61(z0), x1)) → c72(U41'(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(U41(U71(z0, z1, z2), x1)) → c72(U41'(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(U41(U72(z0, z1, z2), x1)) → c72(U41'(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(U41(x(z0, z1), x1)) → c72(U41'(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(U41(x0, tt)) → c72(U41'(proper(x0), ok(tt)), PROPER(x0))
PROPER(U41(x0, 0)) → c72(U41'(proper(x0), ok(0)), PROPER(x0))
PROPER(U41(tt, x1)) → c72(U41'(ok(tt), proper(x1)), PROPER(x1))
PROPER(U41(0, x1)) → c72(U41'(ok(0), proper(x1)), PROPER(x1))
PROPER(U51(x0, x1, U11(z0, z1))) → c73(U51'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U51(x0, x1, U12(z0))) → c73(U51'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U51(x0, x1, isNat(z0))) → c73(U51'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U51(x0, x1, U21(z0))) → c73(U51'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U51(x0, x1, U31(z0, z1))) → c73(U51'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U51(x0, x1, U32(z0))) → c73(U51'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U51(x0, x1, U41(z0, z1))) → c73(U51'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U51(x0, x1, U51(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U51(x0, x1, U52(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U51(x0, x1, s(z0))) → c73(U51'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U51(x0, x1, plus(z0, z1))) → c73(U51'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U51(x0, x1, U61(z0))) → c73(U51'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U51(x0, x1, U71(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U51(x0, x1, U72(z0, z1, z2))) → c73(U51'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U51(x0, x1, x(z0, z1))) → c73(U51'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U51(x0, U11(z0, z1), x2)) → c73(U51'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U51(x0, U12(z0), x2)) → c73(U51'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U51(x0, isNat(z0), x2)) → c73(U51'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U51(x0, U21(z0), x2)) → c73(U51'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U51(x0, U31(z0, z1), x2)) → c73(U51'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U51(x0, U32(z0), x2)) → c73(U51'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U51(x0, U41(z0, z1), x2)) → c73(U51'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U51(x0, U51(z0, z1, z2), x2)) → c73(U51'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U52(z0, z1, z2), x2)) → c73(U51'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, s(z0), x2)) → c73(U51'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U51(x0, plus(z0, z1), x2)) → c73(U51'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U51(x0, U61(z0), x2)) → c73(U51'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U51(x0, U71(z0, z1, z2), x2)) → c73(U51'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, U72(z0, z1, z2), x2)) → c73(U51'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U51(x0, x(z0, z1), x2)) → c73(U51'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U51(U11(z0, z1), x1, x2)) → c73(U51'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U12(z0), x1, x2)) → c73(U51'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(isNat(z0), x1, x2)) → c73(U51'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U21(z0), x1, x2)) → c73(U51'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U31(z0, z1), x1, x2)) → c73(U51'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U32(z0), x1, x2)) → c73(U51'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U41(z0, z1), x1, x2)) → c73(U51'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U51(z0, z1, z2), x1, x2)) → c73(U51'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U52(z0, z1, z2), x1, x2)) → c73(U51'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(s(z0), x1, x2)) → c73(U51'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(plus(z0, z1), x1, x2)) → c73(U51'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(U61(z0), x1, x2)) → c73(U51'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U51(U71(z0, z1, z2), x1, x2)) → c73(U51'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(U72(z0, z1, z2), x1, x2)) → c73(U51'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U51(x(z0, z1), x1, x2)) → c73(U51'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U51(x0, x1, tt)) → c73(U51'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, x1, 0)) → c73(U51'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U51(x0, tt, x2)) → c73(U51'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(x0, 0, x2)) → c73(U51'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U51(tt, x1, x2)) → c73(U51'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U51(0, x1, x2)) → c73(U51'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, U11(z0, z1))) → c74(U52'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U52(x0, x1, U12(z0))) → c74(U52'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U52(x0, x1, isNat(z0))) → c74(U52'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U52(x0, x1, U21(z0))) → c74(U52'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U52(x0, x1, U31(z0, z1))) → c74(U52'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U52(x0, x1, U32(z0))) → c74(U52'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U52(x0, x1, U41(z0, z1))) → c74(U52'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U52(x0, x1, U51(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U52(x0, x1, U52(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U52(x0, x1, s(z0))) → c74(U52'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U52(x0, x1, plus(z0, z1))) → c74(U52'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U52(x0, x1, U61(z0))) → c74(U52'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U52(x0, x1, U71(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U52(x0, x1, U72(z0, z1, z2))) → c74(U52'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U52(x0, x1, x(z0, z1))) → c74(U52'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U52(x0, U11(z0, z1), x2)) → c74(U52'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U52(x0, U12(z0), x2)) → c74(U52'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U52(x0, isNat(z0), x2)) → c74(U52'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U52(x0, U21(z0), x2)) → c74(U52'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U52(x0, U31(z0, z1), x2)) → c74(U52'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U52(x0, U32(z0), x2)) → c74(U52'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U52(x0, U41(z0, z1), x2)) → c74(U52'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U52(x0, U51(z0, z1, z2), x2)) → c74(U52'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U52(z0, z1, z2), x2)) → c74(U52'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, s(z0), x2)) → c74(U52'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U52(x0, plus(z0, z1), x2)) → c74(U52'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U52(x0, U61(z0), x2)) → c74(U52'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U52(x0, U71(z0, z1, z2), x2)) → c74(U52'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, U72(z0, z1, z2), x2)) → c74(U52'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U52(x0, x(z0, z1), x2)) → c74(U52'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U52(U11(z0, z1), x1, x2)) → c74(U52'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U12(z0), x1, x2)) → c74(U52'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(isNat(z0), x1, x2)) → c74(U52'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U21(z0), x1, x2)) → c74(U52'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U31(z0, z1), x1, x2)) → c74(U52'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U32(z0), x1, x2)) → c74(U52'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U41(z0, z1), x1, x2)) → c74(U52'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U51(z0, z1, z2), x1, x2)) → c74(U52'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U52(z0, z1, z2), x1, x2)) → c74(U52'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(s(z0), x1, x2)) → c74(U52'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(plus(z0, z1), x1, x2)) → c74(U52'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(U61(z0), x1, x2)) → c74(U52'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U52(U71(z0, z1, z2), x1, x2)) → c74(U52'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(U72(z0, z1, z2), x1, x2)) → c74(U52'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U52(x(z0, z1), x1, x2)) → c74(U52'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U52(x0, x1, tt)) → c74(U52'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, x1, 0)) → c74(U52'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U52(x0, tt, x2)) → c74(U52'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(x0, 0, x2)) → c74(U52'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U52(tt, x1, x2)) → c74(U52'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U52(0, x1, x2)) → c74(U52'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(s(U11(z0, z1))) → c75(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(s(U12(z0))) → c75(S(U12(proper(z0))), PROPER(U12(z0)))
PROPER(s(isNat(z0))) → c75(S(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(s(U21(z0))) → c75(S(U21(proper(z0))), PROPER(U21(z0)))
PROPER(s(U31(z0, z1))) → c75(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(s(U32(z0))) → c75(S(U32(proper(z0))), PROPER(U32(z0)))
PROPER(s(U41(z0, z1))) → c75(S(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(s(U51(z0, z1, z2))) → c75(S(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(s(U52(z0, z1, z2))) → c75(S(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(s(s(z0))) → c75(S(s(proper(z0))), PROPER(s(z0)))
PROPER(s(plus(z0, z1))) → c75(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(s(U61(z0))) → c75(S(U61(proper(z0))), PROPER(U61(z0)))
PROPER(s(U71(z0, z1, z2))) → c75(S(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(s(U72(z0, z1, z2))) → c75(S(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(s(x(z0, z1))) → c75(S(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(s(tt)) → c75(S(ok(tt)))
PROPER(s(0)) → c75(S(ok(0)))
PROPER(plus(x0, U11(z0, z1))) → c76(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(plus(x0, U12(z0))) → c76(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(plus(x0, isNat(z0))) → c76(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(plus(x0, U21(z0))) → c76(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(plus(x0, U31(z0, z1))) → c76(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(plus(x0, U32(z0))) → c76(PLUS(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(plus(x0, U41(z0, z1))) → c76(PLUS(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(plus(x0, U51(z0, z1, z2))) → c76(PLUS(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(plus(x0, U52(z0, z1, z2))) → c76(PLUS(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(plus(x0, s(z0))) → c76(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(plus(x0, plus(z0, z1))) → c76(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(plus(x0, U61(z0))) → c76(PLUS(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(plus(x0, U71(z0, z1, z2))) → c76(PLUS(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(plus(x0, U72(z0, z1, z2))) → c76(PLUS(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(plus(x0, x(z0, z1))) → c76(PLUS(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(plus(U11(z0, z1), x1)) → c76(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(plus(U12(z0), x1)) → c76(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(plus(isNat(z0), x1)) → c76(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(plus(U21(z0), x1)) → c76(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(plus(U31(z0, z1), x1)) → c76(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(plus(U32(z0), x1)) → c76(PLUS(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(plus(U41(z0, z1), x1)) → c76(PLUS(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(plus(U51(z0, z1, z2), x1)) → c76(PLUS(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(plus(U52(z0, z1, z2), x1)) → c76(PLUS(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(plus(s(z0), x1)) → c76(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(plus(plus(z0, z1), x1)) → c76(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(plus(U61(z0), x1)) → c76(PLUS(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(plus(U71(z0, z1, z2), x1)) → c76(PLUS(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(plus(U72(z0, z1, z2), x1)) → c76(PLUS(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(plus(x(z0, z1), x1)) → c76(PLUS(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(plus(x0, tt)) → c76(PLUS(proper(x0), ok(tt)), PROPER(x0))
PROPER(plus(x0, 0)) → c76(PLUS(proper(x0), ok(0)), PROPER(x0))
PROPER(plus(tt, x1)) → c76(PLUS(ok(tt), proper(x1)), PROPER(x1))
PROPER(plus(0, x1)) → c76(PLUS(ok(0), proper(x1)), PROPER(x1))
PROPER(U61(U11(z0, z1))) → c77(U61'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
PROPER(U61(U12(z0))) → c77(U61'(U12(proper(z0))), PROPER(U12(z0)))
PROPER(U61(isNat(z0))) → c77(U61'(isNat(proper(z0))), PROPER(isNat(z0)))
PROPER(U61(U21(z0))) → c77(U61'(U21(proper(z0))), PROPER(U21(z0)))
PROPER(U61(U31(z0, z1))) → c77(U61'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
PROPER(U61(U32(z0))) → c77(U61'(U32(proper(z0))), PROPER(U32(z0)))
PROPER(U61(U41(z0, z1))) → c77(U61'(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
PROPER(U61(U51(z0, z1, z2))) → c77(U61'(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
PROPER(U61(U52(z0, z1, z2))) → c77(U61'(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
PROPER(U61(s(z0))) → c77(U61'(s(proper(z0))), PROPER(s(z0)))
PROPER(U61(plus(z0, z1))) → c77(U61'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
PROPER(U61(U61(z0))) → c77(U61'(U61(proper(z0))), PROPER(U61(z0)))
PROPER(U61(U71(z0, z1, z2))) → c77(U61'(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
PROPER(U61(U72(z0, z1, z2))) → c77(U61'(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
PROPER(U61(x(z0, z1))) → c77(U61'(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
PROPER(U61(tt)) → c77(U61'(ok(tt)))
PROPER(U61(0)) → c77(U61'(ok(0)))
PROPER(U71(x0, x1, U11(z0, z1))) → c79(U71'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U71(x0, x1, U12(z0))) → c79(U71'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U71(x0, x1, isNat(z0))) → c79(U71'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U71(x0, x1, U21(z0))) → c79(U71'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U71(x0, x1, U31(z0, z1))) → c79(U71'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U71(x0, x1, U32(z0))) → c79(U71'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U71(x0, x1, U41(z0, z1))) → c79(U71'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U71(x0, x1, U51(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U71(x0, x1, U52(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U71(x0, x1, s(z0))) → c79(U71'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U71(x0, x1, plus(z0, z1))) → c79(U71'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U71(x0, x1, U61(z0))) → c79(U71'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U71(x0, x1, U71(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U71(x0, x1, U72(z0, z1, z2))) → c79(U71'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U71(x0, x1, x(z0, z1))) → c79(U71'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U71(x0, U11(z0, z1), x2)) → c79(U71'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U71(x0, U12(z0), x2)) → c79(U71'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U71(x0, isNat(z0), x2)) → c79(U71'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U71(x0, U21(z0), x2)) → c79(U71'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U71(x0, U31(z0, z1), x2)) → c79(U71'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U71(x0, U32(z0), x2)) → c79(U71'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U71(x0, U41(z0, z1), x2)) → c79(U71'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U71(x0, U51(z0, z1, z2), x2)) → c79(U71'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U52(z0, z1, z2), x2)) → c79(U71'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, s(z0), x2)) → c79(U71'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U71(x0, plus(z0, z1), x2)) → c79(U71'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U71(x0, U61(z0), x2)) → c79(U71'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U71(x0, U71(z0, z1, z2), x2)) → c79(U71'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, U72(z0, z1, z2), x2)) → c79(U71'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U71(x0, x(z0, z1), x2)) → c79(U71'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U71(U11(z0, z1), x1, x2)) → c79(U71'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U12(z0), x1, x2)) → c79(U71'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(isNat(z0), x1, x2)) → c79(U71'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U21(z0), x1, x2)) → c79(U71'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U31(z0, z1), x1, x2)) → c79(U71'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U32(z0), x1, x2)) → c79(U71'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U41(z0, z1), x1, x2)) → c79(U71'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U51(z0, z1, z2), x1, x2)) → c79(U71'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U52(z0, z1, z2), x1, x2)) → c79(U71'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(s(z0), x1, x2)) → c79(U71'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(plus(z0, z1), x1, x2)) → c79(U71'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(U61(z0), x1, x2)) → c79(U71'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U71(U71(z0, z1, z2), x1, x2)) → c79(U71'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(U72(z0, z1, z2), x1, x2)) → c79(U71'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U71(x(z0, z1), x1, x2)) → c79(U71'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U71(x0, x1, tt)) → c79(U71'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, x1, 0)) → c79(U71'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U71(x0, tt, x2)) → c79(U71'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(x0, 0, x2)) → c79(U71'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U71(tt, x1, x2)) → c79(U71'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U71(0, x1, x2)) → c79(U71'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, U11(z0, z1))) → c80(U72'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1)))
PROPER(U72(x0, x1, U12(z0))) → c80(U72'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0)))
PROPER(U72(x0, x1, isNat(z0))) → c80(U72'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0)))
PROPER(U72(x0, x1, U21(z0))) → c80(U72'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0)))
PROPER(U72(x0, x1, U31(z0, z1))) → c80(U72'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1)))
PROPER(U72(x0, x1, U32(z0))) → c80(U72'(proper(x0), proper(x1), U32(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U32(z0)))
PROPER(U72(x0, x1, U41(z0, z1))) → c80(U72'(proper(x0), proper(x1), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1)))
PROPER(U72(x0, x1, U51(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U51(z0, z1, z2)))
PROPER(U72(x0, x1, U52(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U52(z0, z1, z2)))
PROPER(U72(x0, x1, s(z0))) → c80(U72'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0)))
PROPER(U72(x0, x1, plus(z0, z1))) → c80(U72'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1)))
PROPER(U72(x0, x1, U61(z0))) → c80(U72'(proper(x0), proper(x1), U61(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U61(z0)))
PROPER(U72(x0, x1, U71(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U71(z0, z1, z2)))
PROPER(U72(x0, x1, U72(z0, z1, z2))) → c80(U72'(proper(x0), proper(x1), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U72(z0, z1, z2)))
PROPER(U72(x0, x1, x(z0, z1))) → c80(U72'(proper(x0), proper(x1), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(x(z0, z1)))
PROPER(U72(x0, U11(z0, z1), x2)) → c80(U72'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2))
PROPER(U72(x0, U12(z0), x2)) → c80(U72'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2))
PROPER(U72(x0, isNat(z0), x2)) → c80(U72'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2))
PROPER(U72(x0, U21(z0), x2)) → c80(U72'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2))
PROPER(U72(x0, U31(z0, z1), x2)) → c80(U72'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2))
PROPER(U72(x0, U32(z0), x2)) → c80(U72'(proper(x0), U32(proper(z0)), proper(x2)), PROPER(x0), PROPER(U32(z0)), PROPER(x2))
PROPER(U72(x0, U41(z0, z1), x2)) → c80(U72'(proper(x0), U41(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1)), PROPER(x2))
PROPER(U72(x0, U51(z0, z1, z2), x2)) → c80(U72'(proper(x0), U51(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U51(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U52(z0, z1, z2), x2)) → c80(U72'(proper(x0), U52(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U52(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, s(z0), x2)) → c80(U72'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2))
PROPER(U72(x0, plus(z0, z1), x2)) → c80(U72'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2))
PROPER(U72(x0, U61(z0), x2)) → c80(U72'(proper(x0), U61(proper(z0)), proper(x2)), PROPER(x0), PROPER(U61(z0)), PROPER(x2))
PROPER(U72(x0, U71(z0, z1, z2), x2)) → c80(U72'(proper(x0), U71(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U71(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, U72(z0, z1, z2), x2)) → c80(U72'(proper(x0), U72(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U72(z0, z1, z2)), PROPER(x2))
PROPER(U72(x0, x(z0, z1), x2)) → c80(U72'(proper(x0), x(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(x(z0, z1)), PROPER(x2))
PROPER(U72(U11(z0, z1), x1, x2)) → c80(U72'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U12(z0), x1, x2)) → c80(U72'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(isNat(z0), x1, x2)) → c80(U72'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U21(z0), x1, x2)) → c80(U72'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U31(z0, z1), x1, x2)) → c80(U72'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U32(z0), x1, x2)) → c80(U72'(U32(proper(z0)), proper(x1), proper(x2)), PROPER(U32(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U41(z0, z1), x1, x2)) → c80(U72'(U41(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U41(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U51(z0, z1, z2), x1, x2)) → c80(U72'(U51(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U51(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U52(z0, z1, z2), x1, x2)) → c80(U72'(U52(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U52(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(s(z0), x1, x2)) → c80(U72'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(plus(z0, z1), x1, x2)) → c80(U72'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(U61(z0), x1, x2)) → c80(U72'(U61(proper(z0)), proper(x1), proper(x2)), PROPER(U61(z0)), PROPER(x1), PROPER(x2))
PROPER(U72(U71(z0, z1, z2), x1, x2)) → c80(U72'(U71(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U71(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(U72(z0, z1, z2), x1, x2)) → c80(U72'(U72(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U72(z0, z1, z2)), PROPER(x1), PROPER(x2))
PROPER(U72(x(z0, z1), x1, x2)) → c80(U72'(x(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(x(z0, z1)), PROPER(x1), PROPER(x2))
PROPER(U72(x0, x1, tt)) → c80(U72'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, x1, 0)) → c80(U72'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1))
PROPER(U72(x0, tt, x2)) → c80(U72'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(x0, 0, x2)) → c80(U72'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2))
PROPER(U72(tt, x1, x2)) → c80(U72'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(U72(0, x1, x2)) → c80(U72'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
PROPER(x(x0, U11(z0, z1))) → c81(X(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1)))
PROPER(x(x0, U12(z0))) → c81(X(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0)))
PROPER(x(x0, isNat(z0))) → c81(X(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0)))
PROPER(x(x0, U21(z0))) → c81(X(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0)))
PROPER(x(x0, U31(z0, z1))) → c81(X(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1)))
PROPER(x(x0, U32(z0))) → c81(X(proper(x0), U32(proper(z0))), PROPER(x0), PROPER(U32(z0)))
PROPER(x(x0, U41(z0, z1))) → c81(X(proper(x0), U41(proper(z0), proper(z1))), PROPER(x0), PROPER(U41(z0, z1)))
PROPER(x(x0, U51(z0, z1, z2))) → c81(X(proper(x0), U51(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U51(z0, z1, z2)))
PROPER(x(x0, U52(z0, z1, z2))) → c81(X(proper(x0), U52(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U52(z0, z1, z2)))
PROPER(x(x0, s(z0))) → c81(X(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0)))
PROPER(x(x0, plus(z0, z1))) → c81(X(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1)))
PROPER(x(x0, U61(z0))) → c81(X(proper(x0), U61(proper(z0))), PROPER(x0), PROPER(U61(z0)))
PROPER(x(x0, U71(z0, z1, z2))) → c81(X(proper(x0), U71(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U71(z0, z1, z2)))
PROPER(x(x0, U72(z0, z1, z2))) → c81(X(proper(x0), U72(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U72(z0, z1, z2)))
PROPER(x(x0, x(z0, z1))) → c81(X(proper(x0), x(proper(z0), proper(z1))), PROPER(x0), PROPER(x(z0, z1)))
PROPER(x(U11(z0, z1), x1)) → c81(X(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1))
PROPER(x(U12(z0), x1)) → c81(X(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1))
PROPER(x(isNat(z0), x1)) → c81(X(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1))
PROPER(x(U21(z0), x1)) → c81(X(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1))
PROPER(x(U31(z0, z1), x1)) → c81(X(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1))
PROPER(x(U32(z0), x1)) → c81(X(U32(proper(z0)), proper(x1)), PROPER(U32(z0)), PROPER(x1))
PROPER(x(U41(z0, z1), x1)) → c81(X(U41(proper(z0), proper(z1)), proper(x1)), PROPER(U41(z0, z1)), PROPER(x1))
PROPER(x(U51(z0, z1, z2), x1)) → c81(X(U51(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U51(z0, z1, z2)), PROPER(x1))
PROPER(x(U52(z0, z1, z2), x1)) → c81(X(U52(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U52(z0, z1, z2)), PROPER(x1))
PROPER(x(s(z0), x1)) → c81(X(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1))
PROPER(x(plus(z0, z1), x1)) → c81(X(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1))
PROPER(x(U61(z0), x1)) → c81(X(U61(proper(z0)), proper(x1)), PROPER(U61(z0)), PROPER(x1))
PROPER(x(U71(z0, z1, z2), x1)) → c81(X(U71(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U71(z0, z1, z2)), PROPER(x1))
PROPER(x(U72(z0, z1, z2), x1)) → c81(X(U72(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U72(z0, z1, z2)), PROPER(x1))
PROPER(x(x(z0, z1), x1)) → c81(X(x(proper(z0), proper(z1)), proper(x1)), PROPER(x(z0, z1)), PROPER(x1))
PROPER(x(x0, tt)) → c81(X(proper(x0), ok(tt)), PROPER(x0))
PROPER(x(x0, 0)) → c81(X(proper(x0), ok(0)), PROPER(x0))
PROPER(x(tt, x1)) → c81(X(ok(tt), proper(x1)), PROPER(x1))
PROPER(x(0, x1)) → c81(X(ok(0), proper(x1)), PROPER(x1))
TOP(mark(U11(z0, z1))) → c83(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1)))
TOP(mark(U12(z0))) → c83(TOP(U12(proper(z0))), PROPER(U12(z0)))
TOP(mark(isNat(z0))) → c83(TOP(isNat(proper(z0))), PROPER(isNat(z0)))
TOP(mark(U21(z0))) → c83(TOP(U21(proper(z0))), PROPER(U21(z0)))
TOP(mark(U31(z0, z1))) → c83(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1)))
TOP(mark(U32(z0))) → c83(TOP(U32(proper(z0))), PROPER(U32(z0)))
TOP(mark(U41(z0, z1))) → c83(TOP(U41(proper(z0), proper(z1))), PROPER(U41(z0, z1)))
TOP(mark(U51(z0, z1, z2))) → c83(TOP(U51(proper(z0), proper(z1), proper(z2))), PROPER(U51(z0, z1, z2)))
TOP(mark(U52(z0, z1, z2))) → c83(TOP(U52(proper(z0), proper(z1), proper(z2))), PROPER(U52(z0, z1, z2)))
TOP(mark(s(z0))) → c83(TOP(s(proper(z0))), PROPER(s(z0)))
TOP(mark(plus(z0, z1))) → c83(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1)))
TOP(mark(U61(z0))) → c83(TOP(U61(proper(z0))), PROPER(U61(z0)))
TOP(mark(U71(z0, z1, z2))) → c83(TOP(U71(proper(z0), proper(z1), proper(z2))), PROPER(U71(z0, z1, z2)))
TOP(mark(U72(z0, z1, z2))) → c83(TOP(U72(proper(z0), proper(z1), proper(z2))), PROPER(U72(z0, z1, z2)))
TOP(mark(x(z0, z1))) → c83(TOP(x(proper(z0), proper(z1))), PROPER(x(z0, z1)))
TOP(ok(U11(tt, z0))) → c84(TOP(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0)))
TOP(ok(U31(tt, z0))) → c84(TOP(mark(U32(isNat(z0)))), ACTIVE(U31(tt, z0)))
TOP(ok(U41(tt, z0))) → c84(TOP(mark(z0)), ACTIVE(U41(tt, z0)))
TOP(ok(U51(tt, z0, z1))) → c84(TOP(mark(U52(isNat(z1), z0, z1))), ACTIVE(U51(tt, z0, z1)))
TOP(ok(U52(tt, z0, z1))) → c84(TOP(mark(s(plus(z1, z0)))), ACTIVE(U52(tt, z0, z1)))
TOP(ok(U71(tt, z0, z1))) → c84(TOP(mark(U72(isNat(z1), z0, z1))), ACTIVE(U71(tt, z0, z1)))
TOP(ok(U72(tt, z0, z1))) → c84(TOP(mark(plus(x(z1, z0), z1))), ACTIVE(U72(tt, z0, z1)))
TOP(ok(isNat(plus(z0, z1)))) → c84(TOP(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1))))
TOP(ok(isNat(s(z0)))) → c84(TOP(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0))))
TOP(ok(isNat(x(z0, z1)))) → c84(TOP(mark(U31(isNat(z0), z1))), ACTIVE(isNat(x(z0, z1))))
TOP(ok(plus(z0, 0))) → c84(TOP(mark(U41(isNat(z0), z0))), ACTIVE(plus(z0, 0)))
TOP(ok(plus(z0, s(z1)))) → c84(TOP(mark(U51(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1))))
TOP(ok(x(z0, 0))) → c84(TOP(mark(U61(isNat(z0)))), ACTIVE(x(z0, 0)))
TOP(ok(x(z0, s(z1)))) → c84(TOP(mark(U71(isNat(z1), z1, z0))), ACTIVE(x(z0, s(z1))))
TOP(ok(U11(z0, z1))) → c84(TOP(U11(active(z0), z1)), ACTIVE(U11(z0, z1)))
TOP(ok(U12(z0))) → c84(TOP(U12(active(z0))), ACTIVE(U12(z0)))
TOP(ok(U21(z0))) → c84(TOP(U21(active(z0))), ACTIVE(U21(z0)))
TOP(ok(U31(z0, z1))) → c84(TOP(U31(active(z0), z1)), ACTIVE(U31(z0, z1)))
TOP(ok(U32(z0))) → c84(TOP(U32(active(z0))), ACTIVE(U32(z0)))
TOP(ok(U41(z0, z1))) → c84(TOP(U41(active(z0), z1)), ACTIVE(U41(z0, z1)))
TOP(ok(U51(z0, z1, z2))) → c84(TOP(U51(active(z0), z1, z2)), ACTIVE(U51(z0, z1, z2)))
TOP(ok(U52(z0, z1, z2))) → c84(TOP(U52(active(z0), z1, z2)), ACTIVE(U52(z0, z1, z2)))
TOP(ok(s(z0))) → c84(TOP(s(active(z0))), ACTIVE(s(z0)))
TOP(ok(plus(z0, z1))) → c84(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1)))
TOP(ok(plus(z0, z1))) → c84(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
TOP(ok(U61(z0))) → c84(TOP(U61(active(z0))), ACTIVE(U61(z0)))
TOP(ok(U71(z0, z1, z2))) → c84(TOP(U71(active(z0), z1, z2)), ACTIVE(U71(z0, z1, z2)))
TOP(ok(U72(z0, z1, z2))) → c84(TOP(U72(active(z0), z1, z2)), ACTIVE(U72(z0, z1, z2)))
TOP(ok(x(z0, z1))) → c84(TOP(x(active(z0), z1)), ACTIVE(x(z0, z1)))
TOP(ok(x(z0, z1))) → c84(TOP(x(z0, active(z1))), ACTIVE(x(z0, z1)))
(152) Obligation:
Complexity Dependency Tuples Problem
Rules:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
K tuples:none
Defined Rule Symbols:
active, U12, isNat, U32, U52, s, plus, U72, x, U11, U31, U41, U61, U21, U51, U71, proper
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(153) CdtUsableRulesProof (EQUIVALENT transformation)
The following rules are not usable and were removed:
active(U11(tt, z0)) → mark(U12(isNat(z0)))
active(U12(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt, z0)) → mark(U32(isNat(z0)))
active(U32(tt)) → mark(tt)
active(U41(tt, z0)) → mark(z0)
active(U51(tt, z0, z1)) → mark(U52(isNat(z1), z0, z1))
active(U52(tt, z0, z1)) → mark(s(plus(z1, z0)))
active(U61(tt)) → mark(0)
active(U71(tt, z0, z1)) → mark(U72(isNat(z1), z0, z1))
active(U72(tt, z0, z1)) → mark(plus(x(z1, z0), z1))
active(isNat(0)) → mark(tt)
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1))
active(isNat(s(z0))) → mark(U21(isNat(z0)))
active(isNat(x(z0, z1))) → mark(U31(isNat(z0), z1))
active(plus(z0, 0)) → mark(U41(isNat(z0), z0))
active(plus(z0, s(z1))) → mark(U51(isNat(z1), z1, z0))
active(x(z0, 0)) → mark(U61(isNat(z0)))
active(x(z0, s(z1))) → mark(U71(isNat(z1), z1, z0))
active(U11(z0, z1)) → U11(active(z0), z1)
active(U12(z0)) → U12(active(z0))
active(U21(z0)) → U21(active(z0))
active(U31(z0, z1)) → U31(active(z0), z1)
active(U32(z0)) → U32(active(z0))
active(U41(z0, z1)) → U41(active(z0), z1)
active(U51(z0, z1, z2)) → U51(active(z0), z1, z2)
active(U52(z0, z1, z2)) → U52(active(z0), z1, z2)
active(s(z0)) → s(active(z0))
active(plus(z0, z1)) → plus(active(z0), z1)
active(plus(z0, z1)) → plus(z0, active(z1))
active(U61(z0)) → U61(active(z0))
active(U71(z0, z1, z2)) → U71(active(z0), z1, z2)
active(U72(z0, z1, z2)) → U72(active(z0), z1, z2)
active(x(z0, z1)) → x(active(z0), z1)
active(x(z0, z1)) → x(z0, active(z1))
U12(mark(z0)) → mark(U12(z0))
U12(ok(z0)) → ok(U12(z0))
isNat(ok(z0)) → ok(isNat(z0))
U32(mark(z0)) → mark(U32(z0))
U32(ok(z0)) → ok(U32(z0))
U52(mark(z0), z1, z2) → mark(U52(z0, z1, z2))
U52(ok(z0), ok(z1), ok(z2)) → ok(U52(z0, z1, z2))
s(mark(z0)) → mark(s(z0))
s(ok(z0)) → ok(s(z0))
plus(mark(z0), z1) → mark(plus(z0, z1))
plus(z0, mark(z1)) → mark(plus(z0, z1))
plus(ok(z0), ok(z1)) → ok(plus(z0, z1))
U72(mark(z0), z1, z2) → mark(U72(z0, z1, z2))
U72(ok(z0), ok(z1), ok(z2)) → ok(U72(z0, z1, z2))
x(mark(z0), z1) → mark(x(z0, z1))
x(z0, mark(z1)) → mark(x(z0, z1))
x(ok(z0), ok(z1)) → ok(x(z0, z1))
U11(mark(z0), z1) → mark(U11(z0, z1))
U11(ok(z0), ok(z1)) → ok(U11(z0, z1))
U31(mark(z0), z1) → mark(U31(z0, z1))
U31(ok(z0), ok(z1)) → ok(U31(z0, z1))
U41(mark(z0), z1) → mark(U41(z0, z1))
U41(ok(z0), ok(z1)) → ok(U41(z0, z1))
U61(mark(z0)) → mark(U61(z0))
U61(ok(z0)) → ok(U61(z0))
U21(mark(z0)) → mark(U21(z0))
U21(ok(z0)) → ok(U21(z0))
U51(mark(z0), z1, z2) → mark(U51(z0, z1, z2))
U51(ok(z0), ok(z1), ok(z2)) → ok(U51(z0, z1, z2))
U71(mark(z0), z1, z2) → mark(U71(z0, z1, z2))
U71(ok(z0), ok(z1), ok(z2)) → ok(U71(z0, z1, z2))
proper(U11(z0, z1)) → U11(proper(z0), proper(z1))
proper(tt) → ok(tt)
proper(U12(z0)) → U12(proper(z0))
proper(isNat(z0)) → isNat(proper(z0))
proper(U21(z0)) → U21(proper(z0))
proper(U31(z0, z1)) → U31(proper(z0), proper(z1))
proper(U32(z0)) → U32(proper(z0))
proper(U41(z0, z1)) → U41(proper(z0), proper(z1))
proper(U51(z0, z1, z2)) → U51(proper(z0), proper(z1), proper(z2))
proper(U52(z0, z1, z2)) → U52(proper(z0), proper(z1), proper(z2))
proper(s(z0)) → s(proper(z0))
proper(plus(z0, z1)) → plus(proper(z0), proper(z1))
proper(U61(z0)) → U61(proper(z0))
proper(0) → ok(0)
proper(U71(z0, z1, z2)) → U71(proper(z0), proper(z1), proper(z2))
proper(U72(z0, z1, z2)) → U72(proper(z0), proper(z1), proper(z2))
proper(x(z0, z1)) → x(proper(z0), proper(z1))
(154) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
K tuples:none
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(155) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = 0
POL(PLUS(x1, x2)) = [4]x1
POL(S(x1)) = [2]x1
POL(U11'(x1, x2)) = 0
POL(U12'(x1)) = 0
POL(U21'(x1)) = 0
POL(U31'(x1, x2)) = [3]x1 + [2]x2
POL(U32'(x1)) = 0
POL(U41'(x1, x2)) = 0
POL(U51'(x1, x2, x3)) = 0
POL(U52'(x1, x2, x3)) = 0
POL(U61'(x1)) = 0
POL(U71'(x1, x2, x3)) = 0
POL(U72'(x1, x2, x3)) = 0
POL(X(x1, x2)) = 0
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = [4] + x1
POL(ok(x1)) = [1] + x1
(156) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(157) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = x1
POL(PLUS(x1, x2)) = 0
POL(S(x1)) = 0
POL(U11'(x1, x2)) = 0
POL(U12'(x1)) = 0
POL(U21'(x1)) = 0
POL(U31'(x1, x2)) = 0
POL(U32'(x1)) = 0
POL(U41'(x1, x2)) = 0
POL(U51'(x1, x2, x3)) = 0
POL(U52'(x1, x2, x3)) = [4]x2
POL(U61'(x1)) = 0
POL(U71'(x1, x2, x3)) = 0
POL(U72'(x1, x2, x3)) = [2]x2
POL(X(x1, x2)) = 0
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = 0
POL(ok(x1)) = [1] + x1
(158) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(159) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = [2]x1
POL(PLUS(x1, x2)) = 0
POL(S(x1)) = 0
POL(U11'(x1, x2)) = 0
POL(U12'(x1)) = 0
POL(U21'(x1)) = 0
POL(U31'(x1, x2)) = 0
POL(U32'(x1)) = 0
POL(U41'(x1, x2)) = 0
POL(U51'(x1, x2, x3)) = 0
POL(U52'(x1, x2, x3)) = [5]x2
POL(U61'(x1)) = 0
POL(U71'(x1, x2, x3)) = x2
POL(U72'(x1, x2, x3)) = [4]x2
POL(X(x1, x2)) = 0
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = [5]
POL(ok(x1)) = [1] + x1
(160) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(161) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = [4]x1
POL(PLUS(x1, x2)) = 0
POL(S(x1)) = 0
POL(U11'(x1, x2)) = 0
POL(U12'(x1)) = 0
POL(U21'(x1)) = 0
POL(U31'(x1, x2)) = 0
POL(U32'(x1)) = 0
POL(U41'(x1, x2)) = 0
POL(U51'(x1, x2, x3)) = x2 + x3
POL(U52'(x1, x2, x3)) = [3]x2 + [3]x3
POL(U61'(x1)) = 0
POL(U71'(x1, x2, x3)) = [3]x2 + [4]x3
POL(U72'(x1, x2, x3)) = [4]x2 + [3]x3
POL(X(x1, x2)) = 0
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = [3]
POL(ok(x1)) = [1] + x1
(162) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(163) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
X(mark(z0), z1) → c62(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = [2]x1
POL(PLUS(x1, x2)) = [2]x1
POL(S(x1)) = 0
POL(U11'(x1, x2)) = 0
POL(U12'(x1)) = 0
POL(U21'(x1)) = 0
POL(U31'(x1, x2)) = [2]x1 + [3]x2
POL(U32'(x1)) = 0
POL(U41'(x1, x2)) = 0
POL(U51'(x1, x2, x3)) = 0
POL(U52'(x1, x2, x3)) = [2]x2
POL(U61'(x1)) = 0
POL(U71'(x1, x2, x3)) = [3]x2
POL(U72'(x1, x2, x3)) = [2]x2 + [3]x3
POL(X(x1, x2)) = [2]x1
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = [1] + x1
POL(ok(x1)) = [2] + x1
(164) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(z0, mark(z1)) → c63(X(z0, z1))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(165) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = [2]x1
POL(PLUS(x1, x2)) = 0
POL(S(x1)) = 0
POL(U11'(x1, x2)) = [4]x2
POL(U12'(x1)) = 0
POL(U21'(x1)) = 0
POL(U31'(x1, x2)) = [4]x2
POL(U32'(x1)) = 0
POL(U41'(x1, x2)) = x2
POL(U51'(x1, x2, x3)) = [3]x2 + [2]x3
POL(U52'(x1, x2, x3)) = x2 + [2]x3
POL(U61'(x1)) = 0
POL(U71'(x1, x2, x3)) = [4]x3
POL(U72'(x1, x2, x3)) = [3]x3
POL(X(x1, x2)) = 0
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = 0
POL(ok(x1)) = [4] + x1
(166) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(z0, mark(z1)) → c63(X(z0, z1))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(167) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U32'(ok(z0)) → c44(U32'(z0))
U61'(ok(z0)) → c57(U61'(z0))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = [2]x1
POL(PLUS(x1, x2)) = 0
POL(S(x1)) = 0
POL(U11'(x1, x2)) = [4]x2
POL(U12'(x1)) = 0
POL(U21'(x1)) = 0
POL(U31'(x1, x2)) = 0
POL(U32'(x1)) = [4]x1
POL(U41'(x1, x2)) = 0
POL(U51'(x1, x2, x3)) = 0
POL(U52'(x1, x2, x3)) = [4]x3
POL(U61'(x1)) = [4]x1
POL(U71'(x1, x2, x3)) = [3]x2
POL(U72'(x1, x2, x3)) = 0
POL(X(x1, x2)) = 0
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = x1
POL(ok(x1)) = [4] + x1
(168) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(z0, mark(z1)) → c63(X(z0, z1))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U32'(ok(z0)) → c44(U32'(z0))
U61'(ok(z0)) → c57(U61'(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(169) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(z0, mark(z1)) → c63(X(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = 0
POL(PLUS(x1, x2)) = [2]x1
POL(S(x1)) = 0
POL(U11'(x1, x2)) = [3]x2
POL(U12'(x1)) = 0
POL(U21'(x1)) = 0
POL(U31'(x1, x2)) = [2]x2
POL(U32'(x1)) = 0
POL(U41'(x1, x2)) = 0
POL(U51'(x1, x2, x3)) = [2]x2 + [4]x3
POL(U52'(x1, x2, x3)) = [3]x2
POL(U61'(x1)) = 0
POL(U71'(x1, x2, x3)) = [2]x2 + [2]x3
POL(U72'(x1, x2, x3)) = [2]x1 + [2]x2 + [2]x3
POL(X(x1, x2)) = [4]x1 + x2
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = [1] + x1
POL(ok(x1)) = [4] + x1
(170) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U32'(ok(z0)) → c44(U32'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(z0, mark(z1)) → c63(X(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(171) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U41'(mark(z0), z1) → c45(U41'(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = 0
POL(PLUS(x1, x2)) = [2]x1
POL(S(x1)) = 0
POL(U11'(x1, x2)) = 0
POL(U12'(x1)) = 0
POL(U21'(x1)) = 0
POL(U31'(x1, x2)) = 0
POL(U32'(x1)) = 0
POL(U41'(x1, x2)) = x1
POL(U51'(x1, x2, x3)) = [2]x3
POL(U52'(x1, x2, x3)) = [2]x2
POL(U61'(x1)) = 0
POL(U71'(x1, x2, x3)) = 0
POL(U72'(x1, x2, x3)) = [2]x2 + [4]x3
POL(X(x1, x2)) = 0
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = [1] + x1
POL(ok(x1)) = x1
(172) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U32'(ok(z0)) → c44(U32'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(z0, mark(z1)) → c63(X(z0, z1))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(173) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U12'(ok(z0)) → c38(U12'(z0))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = 0
POL(PLUS(x1, x2)) = [3]x1
POL(S(x1)) = 0
POL(U11'(x1, x2)) = 0
POL(U12'(x1)) = x1
POL(U21'(x1)) = 0
POL(U31'(x1, x2)) = [2]x2
POL(U32'(x1)) = 0
POL(U41'(x1, x2)) = [2]x1
POL(U51'(x1, x2, x3)) = [2]x2 + [4]x3
POL(U52'(x1, x2, x3)) = [4]x1 + [4]x3
POL(U61'(x1)) = 0
POL(U71'(x1, x2, x3)) = [4]x2
POL(U72'(x1, x2, x3)) = [2]x2
POL(X(x1, x2)) = [4]x1 + [3]x2
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = x1
POL(ok(x1)) = [1] + x1
(174) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U32'(ok(z0)) → c44(U32'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(z0, mark(z1)) → c63(X(z0, z1))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U12'(ok(z0)) → c38(U12'(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(175) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U12'(mark(z0)) → c37(U12'(z0))
U61'(mark(z0)) → c56(U61'(z0))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = 0
POL(PLUS(x1, x2)) = 0
POL(S(x1)) = 0
POL(U11'(x1, x2)) = 0
POL(U12'(x1)) = x1
POL(U21'(x1)) = 0
POL(U31'(x1, x2)) = [2]x2
POL(U32'(x1)) = 0
POL(U41'(x1, x2)) = 0
POL(U51'(x1, x2, x3)) = 0
POL(U52'(x1, x2, x3)) = [2]x3
POL(U61'(x1)) = [4]x1
POL(U71'(x1, x2, x3)) = [2]x2 + [3]x3
POL(U72'(x1, x2, x3)) = 0
POL(X(x1, x2)) = [3]x2
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = [1] + x1
POL(ok(x1)) = [3] + x1
(176) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U32'(ok(z0)) → c44(U32'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(z0, mark(z1)) → c63(X(z0, z1))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U12'(ok(z0)) → c38(U12'(z0))
U12'(mark(z0)) → c37(U12'(z0))
U61'(mark(z0)) → c56(U61'(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(177) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U21'(ok(z0)) → c40(U21'(z0))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = 0
POL(PLUS(x1, x2)) = 0
POL(S(x1)) = [2]x1
POL(U11'(x1, x2)) = 0
POL(U12'(x1)) = 0
POL(U21'(x1)) = x1
POL(U31'(x1, x2)) = [2]x1 + [4]x2
POL(U32'(x1)) = 0
POL(U41'(x1, x2)) = [4]x1 + [3]x2
POL(U51'(x1, x2, x3)) = 0
POL(U52'(x1, x2, x3)) = [2]x2
POL(U61'(x1)) = [4]x1
POL(U71'(x1, x2, x3)) = 0
POL(U72'(x1, x2, x3)) = [4]x2 + [2]x3
POL(X(x1, x2)) = 0
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = x1
POL(ok(x1)) = [1] + x1
(178) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U21'(mark(z0)) → c39(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U32'(ok(z0)) → c44(U32'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(z0, mark(z1)) → c63(X(z0, z1))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U12'(ok(z0)) → c38(U12'(z0))
U12'(mark(z0)) → c37(U12'(z0))
U61'(mark(z0)) → c56(U61'(z0))
U21'(ok(z0)) → c40(U21'(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(179) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U32'(mark(z0)) → c43(U32'(z0))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = [3]x1
POL(PLUS(x1, x2)) = [4]x2
POL(S(x1)) = [4]x1
POL(U11'(x1, x2)) = 0
POL(U12'(x1)) = [2]x1
POL(U21'(x1)) = 0
POL(U31'(x1, x2)) = [4]x1
POL(U32'(x1)) = [2]x1
POL(U41'(x1, x2)) = [4]x1
POL(U51'(x1, x2, x3)) = [4]x2 + [4]x3
POL(U52'(x1, x2, x3)) = [4]x1 + [2]x2 + [4]x3
POL(U61'(x1)) = [4]x1
POL(U71'(x1, x2, x3)) = [4]x2 + [2]x3
POL(U72'(x1, x2, x3)) = [3]x2
POL(X(x1, x2)) = [4]x1 + [3]x2
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = [4] + x1
POL(ok(x1)) = x1
(180) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U21'(mark(z0)) → c39(U21'(z0))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U32'(ok(z0)) → c44(U32'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(z0, mark(z1)) → c63(X(z0, z1))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U12'(ok(z0)) → c38(U12'(z0))
U12'(mark(z0)) → c37(U12'(z0))
U61'(mark(z0)) → c56(U61'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(181) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = [2]x1
POL(PLUS(x1, x2)) = [3]x1 + [2]x2
POL(S(x1)) = [2]x1
POL(U11'(x1, x2)) = [4]x2
POL(U12'(x1)) = 0
POL(U21'(x1)) = 0
POL(U31'(x1, x2)) = 0
POL(U32'(x1)) = 0
POL(U41'(x1, x2)) = [4]x1 + [4]x2
POL(U51'(x1, x2, x3)) = x1 + [2]x2 + [3]x3
POL(U52'(x1, x2, x3)) = [5]x1 + [2]x3
POL(U61'(x1)) = [4]x1
POL(U71'(x1, x2, x3)) = [3]x3
POL(U72'(x1, x2, x3)) = [4]x3
POL(X(x1, x2)) = [2]x2
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = [1] + x1
POL(ok(x1)) = x1
(182) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U21'(mark(z0)) → c39(U21'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U32'(ok(z0)) → c44(U32'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(z0, mark(z1)) → c63(X(z0, z1))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U12'(ok(z0)) → c38(U12'(z0))
U12'(mark(z0)) → c37(U12'(z0))
U61'(mark(z0)) → c56(U61'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(183) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = [3]x1
POL(PLUS(x1, x2)) = [3]x1
POL(S(x1)) = [4]x1
POL(U11'(x1, x2)) = [4]x2
POL(U12'(x1)) = [2]x1
POL(U21'(x1)) = 0
POL(U31'(x1, x2)) = [4]x1
POL(U32'(x1)) = 0
POL(U41'(x1, x2)) = [2]x2
POL(U51'(x1, x2, x3)) = [4]x1 + [4]x2
POL(U52'(x1, x2, x3)) = [4]x1 + [3]x3
POL(U61'(x1)) = 0
POL(U71'(x1, x2, x3)) = x1 + [2]x2 + x3
POL(U72'(x1, x2, x3)) = 0
POL(X(x1, x2)) = 0
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = [1] + x1
POL(ok(x1)) = x1
(184) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U21'(mark(z0)) → c39(U21'(z0))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U32'(ok(z0)) → c44(U32'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(z0, mark(z1)) → c63(X(z0, z1))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U12'(ok(z0)) → c38(U12'(z0))
U12'(mark(z0)) → c37(U12'(z0))
U61'(mark(z0)) → c56(U61'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(185) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U11'(mark(z0), z1) → c35(U11'(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = 0
POL(PLUS(x1, x2)) = [4]x1
POL(S(x1)) = [4]x1
POL(U11'(x1, x2)) = [4]x1 + x2
POL(U12'(x1)) = [4]x1
POL(U21'(x1)) = 0
POL(U31'(x1, x2)) = 0
POL(U32'(x1)) = 0
POL(U41'(x1, x2)) = [3]x2
POL(U51'(x1, x2, x3)) = [2]x1 + [2]x3
POL(U52'(x1, x2, x3)) = [3]x2 + [2]x3
POL(U61'(x1)) = 0
POL(U71'(x1, x2, x3)) = [4]x1 + [4]x2
POL(U72'(x1, x2, x3)) = [2]x1 + [2]x2 + [3]x3
POL(X(x1, x2)) = [4]x2
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = [4] + x1
POL(ok(x1)) = x1
(186) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:
U21'(mark(z0)) → c39(U21'(z0))
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U32'(ok(z0)) → c44(U32'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(z0, mark(z1)) → c63(X(z0, z1))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U12'(ok(z0)) → c38(U12'(z0))
U12'(mark(z0)) → c37(U12'(z0))
U61'(mark(z0)) → c56(U61'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(187) CdtRuleRemovalProof (UPPER BOUND (ADD(O(n^1))) transformation)
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
U21'(mark(z0)) → c39(U21'(z0))
We considered the (Usable) Rules:none
And the Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation :
POL(ISNAT(x1)) = [3]x1
POL(PLUS(x1, x2)) = [4]x2
POL(S(x1)) = 0
POL(U11'(x1, x2)) = x2
POL(U12'(x1)) = 0
POL(U21'(x1)) = x1
POL(U31'(x1, x2)) = [4]x2
POL(U32'(x1)) = [3]x1
POL(U41'(x1, x2)) = 0
POL(U51'(x1, x2, x3)) = [2]x2 + [2]x3
POL(U52'(x1, x2, x3)) = 0
POL(U61'(x1)) = [2]x1
POL(U71'(x1, x2, x3)) = [4]x1 + [3]x2 + [3]x3
POL(U72'(x1, x2, x3)) = [4]x3
POL(X(x1, x2)) = [2]x2
POL(c35(x1)) = x1
POL(c36(x1)) = x1
POL(c37(x1)) = x1
POL(c38(x1)) = x1
POL(c39(x1)) = x1
POL(c40(x1)) = x1
POL(c41(x1)) = x1
POL(c42(x1)) = x1
POL(c43(x1)) = x1
POL(c44(x1)) = x1
POL(c45(x1)) = x1
POL(c46(x1)) = x1
POL(c47(x1)) = x1
POL(c48(x1)) = x1
POL(c49(x1)) = x1
POL(c50(x1)) = x1
POL(c51(x1)) = x1
POL(c52(x1)) = x1
POL(c53(x1)) = x1
POL(c54(x1)) = x1
POL(c55(x1)) = x1
POL(c56(x1)) = x1
POL(c57(x1)) = x1
POL(c58(x1)) = x1
POL(c59(x1)) = x1
POL(c60(x1)) = x1
POL(c61(x1)) = x1
POL(c62(x1)) = x1
POL(c63(x1)) = x1
POL(c64(x1)) = x1
POL(c82(x1)) = x1
POL(mark(x1)) = [1] + x1
POL(ok(x1)) = x1
(188) Obligation:
Complexity Dependency Tuples Problem
Rules:none
Tuples:
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U12'(mark(z0)) → c37(U12'(z0))
U12'(ok(z0)) → c38(U12'(z0))
U21'(mark(z0)) → c39(U21'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
U32'(mark(z0)) → c43(U32'(z0))
U32'(ok(z0)) → c44(U32'(z0))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U61'(mark(z0)) → c56(U61'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(z0, mark(z1)) → c63(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
ISNAT(ok(z0)) → c82(ISNAT(z0))
S tuples:none
K tuples:
U31'(mark(z0), z1) → c41(U31'(z0, z1))
U31'(ok(z0), ok(z1)) → c42(U31'(z0, z1))
S(mark(z0)) → c51(S(z0))
S(ok(z0)) → c52(S(z0))
PLUS(mark(z0), z1) → c53(PLUS(z0, z1))
PLUS(ok(z0), ok(z1)) → c55(PLUS(z0, z1))
U52'(ok(z0), ok(z1), ok(z2)) → c50(U52'(z0, z1, z2))
U72'(ok(z0), ok(z1), ok(z2)) → c61(U72'(z0, z1, z2))
ISNAT(ok(z0)) → c82(ISNAT(z0))
U71'(ok(z0), ok(z1), ok(z2)) → c59(U71'(z0, z1, z2))
U51'(ok(z0), ok(z1), ok(z2)) → c48(U51'(z0, z1, z2))
X(mark(z0), z1) → c62(X(z0, z1))
X(ok(z0), ok(z1)) → c64(X(z0, z1))
U11'(ok(z0), ok(z1)) → c36(U11'(z0, z1))
U41'(ok(z0), ok(z1)) → c46(U41'(z0, z1))
U32'(ok(z0)) → c44(U32'(z0))
U61'(ok(z0)) → c57(U61'(z0))
U72'(mark(z0), z1, z2) → c60(U72'(z0, z1, z2))
X(z0, mark(z1)) → c63(X(z0, z1))
U41'(mark(z0), z1) → c45(U41'(z0, z1))
U12'(ok(z0)) → c38(U12'(z0))
U12'(mark(z0)) → c37(U12'(z0))
U61'(mark(z0)) → c56(U61'(z0))
U21'(ok(z0)) → c40(U21'(z0))
U32'(mark(z0)) → c43(U32'(z0))
U52'(mark(z0), z1, z2) → c49(U52'(z0, z1, z2))
PLUS(z0, mark(z1)) → c54(PLUS(z0, z1))
U51'(mark(z0), z1, z2) → c47(U51'(z0, z1, z2))
U71'(mark(z0), z1, z2) → c58(U71'(z0, z1, z2))
U11'(mark(z0), z1) → c35(U11'(z0, z1))
U21'(mark(z0)) → c39(U21'(z0))
Defined Rule Symbols:none
Defined Pair Symbols:
U11', U12', U21', U31', U32', U41', U51', U52', S, PLUS, U61', U71', U72', X, ISNAT
Compound Symbols:
c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c82
(189) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)
The set S is empty
(190) BOUNDS(O(1), O(1))